diff --git a/.gitignore b/.gitignore index 8a04de1..b0e987b 100644 --- a/.gitignore +++ b/.gitignore @@ -23,6 +23,7 @@ deps/src/ *.aux *.DS_Store *.xdv +*.xcf *.dat *.err *.out @@ -49,4 +50,8 @@ Manifest.toml .vscode .history LocalPreferences.toml -run/ \ No newline at end of file +run/ +results/ +archives/ +benchmark/ +test_runs/ \ No newline at end of file diff --git a/example/freeE/plot_freeE.jl b/example/freeE/plot_freeE.jl index 8ab7b57..3e01fe2 100644 --- a/example/freeE/plot_freeE.jl +++ b/example/freeE/plot_freeE.jl @@ -12,7 +12,7 @@ Fs = [-0.0,] # beta = [25.0] beta = [80.0] order = [5,] -const fileName = "freeE_$(dim)d.dat" +const filename = "freeE_$(dim)d.dat" const val_benchmark = cdict = Dict(["blue" => "#0077BB", "cyan" => "#33BBEE", "teal" => "#009988", "orange" => "#EE7733", "red" => "#CC3311", "magenta" => "#EE3377", "grey" => "#BBBBBB"]); @@ -53,7 +53,7 @@ end if abspath(PROGRAM_FILE) == @__FILE__ - freeE_data = readdlm(fileName) + freeE_data = readdlm(filename) num_data = size(freeE_data)[1] freeE_total, error_total, mass2_total = [], [], [] diff --git a/example/input.jl b/example/input.jl index f9250bb..b3a2cc6 100644 --- a/example/input.jl +++ b/example/input.jl @@ -1,24 +1,74 @@ -dim = 2. # dimension of the problem -rs = [2.0,] -# mass2 = [1.0, 2.0, 3.0] -mass2 = [0.1,] # screening parameter -Fs = [-0.0,] # Fermi liquid parameter with zero angular momentum -beta = [25.0] # inverse temperature beta = β*E_F -order = [3,] # order of diagrams -neval = 1e6 # number of Monte Carlo samples -# neval = 1e8 -isDynamic = false # whether to use effective field theory with dynamic screening or not -isFock = false # whether to use Fock renormalization or not +# Use finalized lambda scans to determine mass2 for maximum orders N = 4, 5, 6 +include("lambda_scans.jl") +dim = 3 # dimension of the problem +rs = [6.0] +order = [5] # maximum diagram order of the run +mass2 = rs_to_lambdas[dim][order[1]][rs[1]] -diagGenerate = :GV # :GV or :Parquet, algorithm to generate diagrams -# diagGenerate = :Parquet -isLayered2D = true # whether to use layered 2D system or not +Fs = [-0.0] # Fermi liquid parameter with zero angular momentum +beta = [40.0] # inverse temperature beta = β*E_F +neval = 1e11 # number of Monte Carlo samples +isDynamic = false # whether to use effective field theory with dynamic screening or not +isFock = false # whether to use Fock renormalization or not + +diagGenerate = :GV # :GV or :Parquet, algorithm to generate diagrams +isLayered2D = false # whether to use layered 2D system or not spin = 2 # 2 for unpolarized, 1 for polarized spinPolarPara = 2 / spin - 1 # spin-polarization parameter (n_up - n_down) / (n_up + n_down) ∈ [0,1] +ispolarized = spinPolarPara != 0.0 + +println("rs = $rs, mass2 = $mass2, order = $order, neval = $neval") + +# Build file base names +basenames = [ + "para_wn_1minus0", + "data$(dim)d_Z", + "data$(dim)d_K", + "meff_$(dim)d", + "inverse_meff_$(dim)d", + "zfactor_$(dim)d", + "inverse_zfactor_$(dim)d", + "chemical_potential_$(dim)d", + "dispersion_ratio_$(dim)d", + "inverse_dispersion_ratio_$(dim)d", +] +for i in eachindex(basenames) + if spin != 2 + basenames[i] *= "_spin$(spin)" + end + if ispolarized + basenames[i] *= "_polarized" + end + if isLayered2D + @assert dim == 2 "Layered 2D mode is only available for dim = 2!" + basenames[i] *= "_layered2d" + end +end +para_basename, +sigma_z_basename, +sigma_k_basename, +meff_basename, +inverse_meff_basename, +zfactor_basename, +inverse_zfactor_basename, +chemical_potential_basename, +dispersion_ratio_basename, +inverse_dispersion_ratio_basename = basenames + +# Directory paths +data_directory = joinpath(@__DIR__, "sigma/data$(dim)d") +res_directory = joinpath(@__DIR__, "sigma") +para_directory = "" # src directory -if isLayered2D - const parafilename = "para_wn_1minus0_layered2d.csv" -else - const parafilename = "para_wn_1minus0.csv" -end \ No newline at end of file +# File paths +const parafilename = joinpath(para_directory, para_basename * ".csv") +const sigma_z_filename = joinpath(data_directory, sigma_z_basename * ".jld2") +const sigma_k_filename = joinpath(data_directory, sigma_k_basename * ".jld2") +const meff_filename = joinpath(res_directory, meff_basename * ".dat") +const inverse_meff_filename = joinpath(res_directory, inverse_meff_basename * ".dat") +const zfactor_filename = joinpath(res_directory, zfactor_basename * ".dat") +const zinv_filename = joinpath(res_directory, inverse_zfactor_basename * ".dat") +const chemical_potential_filename = joinpath(res_directory, chemical_potential_basename * ".dat") +const dispersion_ratio_filename = joinpath(res_directory, dispersion_ratio_basename * ".dat") +const inverse_dispersion_ratio_filename = joinpath(res_directory, inverse_dispersion_ratio_basename * ".dat") diff --git a/example/lambda_scans.jl b/example/lambda_scans.jl new file mode 100644 index 0000000..51974ab --- /dev/null +++ b/example/lambda_scans.jl @@ -0,0 +1,53 @@ +const LambdaDictType = Dict{Float64, Vector{Float64}} + +# Finalized 3D lambda scans for maximum orders N = 4, 5, 6 +const rs_to_lambdas_3d_N4 = LambdaDictType( + 0.5 => [1.0, 1.5, 2.0, 2.5, 3.0, 3.5, 4.0, 4.5, 5.0, 5.5, 6.0, 6.5, 7.0], + 1.0 => [0.5, 0.75, 1.0, 1.25, 1.5, 1.75, 2.0, 2.5, 3.0, 3.5, 4.0], + 2.0 => [0.5, 0.75, 1.0, 1.25, 1.5, 1.625, 1.75, 1.875, 2.0, 2.5, 3.0], + 3.0 => [0.375, 0.5, 0.625, 0.75, 0.875, 1.0, 1.125, 1.25, 1.5, 1.75, 2.0], + 4.0 => [0.375, 0.5, 0.625, 0.75, 0.875, 1.0, 1.125, 1.25, 1.5, 2.0], + 5.0 => [0.375, 0.5, 0.625, 0.75, 0.8125, 0.875, 0.9375, 1.0, 1.125, 1.25, 1.5], + 6.0 => [0.375, 0.5, 0.75, 1.0, 1.25, 1.5, 1.75, 2.0, 3.0, 4.0, 5.0], +) +const rs_to_lambdas_3d_N5 = LambdaDictType( + 0.5 => [3.0, 3.5, 4.0, 4.5, 5.0], + 1.0 => [1.5, 1.75, 2.0, 3.0, 3.5], + 2.0 => [1.625, 1.75, 1.875, 2.0, 2.125, 2.25, 2.5], + 3.0 => [1.0, 1.125, 1.25, 1.5, 1.75, 2.0], + 4.0 => [0.875, 1.0, 1.125, 1.25, 1.5, 2.0], + 5.0 => [0.8125, 0.875, 0.9375, 1.0, 1.125], + 6.0 => [0.625, 0.75, 0.875, 1.0, 1.125, 1.25], +) +const rs_to_lambdas_3d_N6 = LambdaDictType() # TODO: Add N = 6 3D lambda scans and datfile entries + +# TODO: Add N = 4, 5, 6 2D lambda scans and datfiles +const rs_to_lambdas_2d_N4 = LambdaDictType() +const rs_to_lambdas_2d_N5 = LambdaDictType() +const rs_to_lambdas_2d_N6 = LambdaDictType() + +""" +Dict of dict of 3D lambda scans vs N and rs (usage: `rs_to_lambdas_3d[N][rs]`). +""" +const rs_to_lambdas_3d = Dict( + 4 => rs_to_lambdas_3d_N4, + 5 => rs_to_lambdas_3d_N5, + 6 => rs_to_lambdas_3d_N6, +) + +""" +Dict of dict of 2D lambda scans vs N and rs (usage: `rs_to_lambdas_3d[N][rs]`). +""" +const rs_to_lambdas_2d = Dict( + 4 => rs_to_lambdas_2d_N4, + 5 => rs_to_lambdas_2d_N5, + 6 => rs_to_lambdas_2d_N6, +) + +""" +Dict of dict of dict of lambda scans vs dim, N, and rs (usage: `rs_to_lambdas[dim][N][rs]`). +""" +const rs_to_lambdas = Dict( + 2 => rs_to_lambdas_2d, + 3 => rs_to_lambdas_3d, +) \ No newline at end of file diff --git a/example/sigma/data3d/para.csv b/example/sigma/data3d/para.csv new file mode 100644 index 0000000..c6e3047 --- /dev/null +++ b/example/sigma/data3d/para.csv @@ -0,0 +1,2131 @@ +Fa,Fs,beta,dim,isDynamic,isFock,mass2,massratio,order,partition,rs,spin,Σw,Σw.err,μ,μ.err +-0.0,-0.0,40.0,3,false,false,0.5,1.0,4,121,1.0,2,0.0,8.148023487204334e-11,0.0002669076991651777,2.5066561790458436e-5 +-0.0,-0.0,40.0,3,false,false,0.5,1.0,4,400,1.0,2,1.8298314792943013,0.0014434830302935014,0.15317190829036337,0.0016129661181684188 +-0.0,-0.0,40.0,3,false,false,0.5,1.0,4,102,1.0,2,0.0,8.148023487204334e-11,0.06829664727101453,2.783294774931405e-5 +-0.0,-0.0,40.0,3,false,false,0.5,1.0,4,110,1.0,2,0.0,8.148023487204334e-11,0.28374062628922664,9.831082603490253e-5 +-0.0,-0.0,40.0,3,false,false,0.5,1.0,4,200,1.0,2,0.20762906277307436,6.673435464263189e-5,0.3303784820461923,0.00025192877441864575 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+-0.0,-0.0,40.0,3,false,false,0.9375,1.0,5,103,5.0,2,0.0,3.39500978633514e-10,0.01190211571252442,3.641134937725902e-6 +-0.0,-0.0,40.0,3,false,false,0.9375,1.0,5,220,5.0,2,-0.39653143290548737,0.031186920255306224,0.08203116925552939,0.010290695879358372 +-0.0,-0.0,40.0,3,false,false,0.9375,1.0,5,113,5.0,2,0.0,3.39500978633514e-10,0.10615863505782512,3.061615662114702e-5 +-0.0,-0.0,40.0,3,false,false,0.9375,1.0,5,301,5.0,2,-0.0241054721228119,4.5611171166797154e-5,0.003390517159353183,1.5168848497090505e-5 +-0.0,-0.0,40.0,3,false,false,0.9375,1.0,5,230,5.0,2,0.7789569633793879,2.8338235040637456,-0.3523616384288215,1.0102213401178166 +-0.0,-0.0,40.0,3,false,false,0.9375,1.0,5,100,5.0,2,0.0,2.0370058718010834e-9,0.020738776008940293,7.1013617052868195e-6 diff --git a/example/sigma/derive_chemical_potential.jl b/example/sigma/derive_chemical_potential.jl new file mode 100644 index 0000000..2da4035 --- /dev/null +++ b/example/sigma/derive_chemical_potential.jl @@ -0,0 +1,29 @@ +using UniElectronGas, ElectronLiquid +using JLD2, DelimitedFiles + +include("../input.jl") + +if abspath(PROGRAM_FILE) == @__FILE__ + isSave = false + if length(ARGS) >= 1 && (ARGS[1] == "s" || ARGS[1] == "-s" || ARGS[1] == "--save" || ARGS[1] == " save") + # the second parameter may be set to save the derived parameters + isSave = true + end + + results = Any[] + for (_rs, _mass2, _F, _beta, _order) in Iterators.product(rs, mass2, Fs, beta, order) + para = ParaMC(rs=_rs, beta=_beta, Fs=_F, order=_order, mass2=_mass2, isDynamic=isDynamic, dim=dim, spin=spin) + try + dmu = UniElectronGas.getdmu(para; parafile=parafilename) + push!(results, Any[_rs, _beta, _mass2, _order, spinPolarPara, dmu...]) + catch + println("No dmu data found for key $(UEG.short(para)) in CSV file $(parafilename)!") + end + end + if isSave + println(chemical_potential_filename) + open(chemical_potential_filename, "a+") do io + writedlm(io, results) + end + end +end diff --git a/example/sigma/derive_dispersion_ratio.jl b/example/sigma/derive_dispersion_ratio.jl new file mode 100644 index 0000000..c733b9f --- /dev/null +++ b/example/sigma/derive_dispersion_ratio.jl @@ -0,0 +1,36 @@ +using UniElectronGas, ElectronLiquid +using JLD2, DelimitedFiles + +include("../input.jl") + +if abspath(PROGRAM_FILE) == @__FILE__ + isSave = false + if length(ARGS) >= 1 && (ARGS[1] == "s" || ARGS[1] == "-s" || ARGS[1] == "--save" || ARGS[1] == " save") + # the second parameter may be set to save the derived parameters + isSave = true + end + + f = jldopen(sigma_k_filename, "r") + results = Any[] + for (_rs, _mass2, _F, _beta, _order) in Iterators.product(rs, mass2, Fs, beta, order) + para = ParaMC(rs=_rs, beta=_beta, Fs=_F, order=_order, mass2=_mass2, isDynamic=isDynamic, dim=dim, spin=spin) + kF = para.kF + for key in keys(f) + loadpara = ParaMC(key) + if UEG.paraid(loadpara) == UEG.paraid(para) + println(UEG.paraid(para)) + + ngrid, kgrid, rSw_k, iSw_k = UniElectronGas.getSigma(para, sigma_k_filename; parafile=parafilename) + dispersion_ratio, fit_p = UniElectronGas.getDispersionRatio(para, rSw_k, kgrid; parafile=parafilename) + println("ϵ_qp / ϵ_0 = ", dispersion_ratio) + push!(results, Any[_rs, _beta, _mass2, _order, dispersion_ratio...]) + writedlm("fit_dispersion.dat", fit_p) + end + end + end + if isSave + open(dispersion_ratio_filename, "a+") do io + writedlm(io, results) + end + end +end diff --git a/example/sigma/derive_everything.sh b/example/sigma/derive_everything.sh new file mode 100644 index 0000000..e5a596d --- /dev/null +++ b/example/sigma/derive_everything.sh @@ -0,0 +1,8 @@ +#!/bin/bash +julia derive_z.jl --save && + julia derive_zinv.jl --save && + julia derive_chemical_potential.jl --save && + julia derive_inverse_dispersion_ratio.jl --save && + julia derive_dispersion_ratio.jl --save && + julia derive_meff.jl --save && + julia derive_meffinv.jl --save diff --git a/example/sigma/derive_inverse_dispersion_ratio.jl b/example/sigma/derive_inverse_dispersion_ratio.jl new file mode 100644 index 0000000..9da4099 --- /dev/null +++ b/example/sigma/derive_inverse_dispersion_ratio.jl @@ -0,0 +1,36 @@ +using UniElectronGas, ElectronLiquid +using JLD2, DelimitedFiles + +include("../input.jl") + +if abspath(PROGRAM_FILE) == @__FILE__ + isSave = false + if length(ARGS) >= 1 && (ARGS[1] == "s" || ARGS[1] == "-s" || ARGS[1] == "--save" || ARGS[1] == " save") + # the second parameter may be set to save the derived parameters + isSave = true + end + + f = jldopen(sigma_k_filename, "r") + results = Any[] + for (_rs, _mass2, _F, _beta, _order) in Iterators.product(rs, mass2, Fs, beta, order) + para = ParaMC(rs=_rs, beta=_beta, Fs=_F, order=_order, mass2=_mass2, isDynamic=isDynamic, dim=dim, spin=spin) + kF = para.kF + for key in keys(f) + loadpara = ParaMC(key) + if UEG.paraid(loadpara) == UEG.paraid(para) + println(UEG.paraid(para)) + + ngrid, kgrid, rSw_k, iSw_k = UniElectronGas.getSigma(para, sigma_k_filename; parafile=parafilename) + dispersion_ratio, fit_p = UniElectronGas.getDispersionRatioInv(para, rSw_k, kgrid; parafile=parafilename) + println("ϵ_qp / ϵ_0 = ", dispersion_ratio) + push!(results, Any[_rs, _beta, _mass2, _order, dispersion_ratio...]) + writedlm("fit_inverse_dispersion.dat", fit_p) + end + end + end + if isSave + open(inverse_dispersion_ratio_filename, "a+") do io + writedlm(io, results) + end + end +end diff --git a/example/sigma/derive_meff.jl b/example/sigma/derive_meff.jl index 642b125..803f72b 100644 --- a/example/sigma/derive_meff.jl +++ b/example/sigma/derive_meff.jl @@ -3,29 +3,6 @@ using JLD2, DelimitedFiles include("../input.jl") -# # dim = 3 -# dim = 2 -# spin = 1 -# # spin = 2 -# # rs = [0.5, 1.0, 2.0] -# rs = [1.0] -# # rs = [0.1, 0.3] -# # mass2 = [0.5, 1.0, 1.5, 2.0, 2.2, 2.4, 2.5, 2.6, 2.8, 3.0, 3.5, 4.0, 4.5, 5.0, 5.5, 6.0] -# # mass2 = [0.5, 1.0, 1.5, 2.0, 2.5, 3.0, 3.5, 4.0, 4.5, 5.0, 5.5] -# mass2 = [1.75] -# Fs = [-0.0,] -# # beta = [25.0,] -# beta = [40.0,] -# order = [4,] -# # order = [5,] -# isDynamic = false -### dSigma/dk = (Sigma[kF_label+idx_dk] - Sigma[kF_label-idx_dk]) / (kgrid[kF_label+idx_dk] - kgrid[kF_label-idx_dk]) - -# const parafilename = "para_wn_1minus0.csv" -const filename = "./data$(dim)d/data$(dim)d_K.jld2" -# const filename = "./data$(dim)d/data$(dim)d_K_o5.jld2" -const savefilename = spin == 2 ? "meff_$(dim)d.dat" : "meff_$(dim)d_spin$spin.dat" - if abspath(PROGRAM_FILE) == @__FILE__ isSave = false if length(ARGS) >= 1 && (ARGS[1] == "s" || ARGS[1] == "-s" || ARGS[1] == "--save" || ARGS[1] == " save") @@ -33,7 +10,7 @@ if abspath(PROGRAM_FILE) == @__FILE__ isSave = true end - f = jldopen(filename, "r") + f = jldopen(sigma_k_filename, "r") results = Any[] for (_rs, _mass2, _F, _beta, _order) in Iterators.product(rs, mass2, Fs, beta, order) para = ParaMC(rs=_rs, beta=_beta, Fs=_F, order=_order, mass2=_mass2, isDynamic=isDynamic, dim=dim, spin=spin) @@ -43,8 +20,8 @@ if abspath(PROGRAM_FILE) == @__FILE__ if UEG.paraid(loadpara) == UEG.paraid(para) println(UEG.paraid(para)) - ngrid, kgrid, rSw_k, iSw_k = UniElectronGas.getSigma(para, filename) - meff, fit_p = UniElectronGas.getMeff(para, rSw_k, kgrid) + ngrid, kgrid, rSw_k, iSw_k = UniElectronGas.getSigma(para, sigma_k_filename; parafile=parafilename) + meff, fit_p = UniElectronGas.getMeff(para, rSw_k, kgrid; parafile=parafilename) # meff = UniElectronGas.getMeff(para, rSw_k, kgrid) println("m* / m = ", meff) push!(results, Any[_rs, _beta, _mass2, _order, meff...]) @@ -53,8 +30,8 @@ if abspath(PROGRAM_FILE) == @__FILE__ end end if isSave - open(savefilename, "a+") do io + open(meff_filename, "a+") do io writedlm(io, results) end end -end \ No newline at end of file +end diff --git a/example/sigma/derive_meffinv.jl b/example/sigma/derive_meffinv.jl new file mode 100644 index 0000000..77cf98d --- /dev/null +++ b/example/sigma/derive_meffinv.jl @@ -0,0 +1,37 @@ +using UniElectronGas, ElectronLiquid +using JLD2, DelimitedFiles + +include("../input.jl") + +if abspath(PROGRAM_FILE) == @__FILE__ + isSave = false + if length(ARGS) >= 1 && (ARGS[1] == "s" || ARGS[1] == "-s" || ARGS[1] == "--save" || ARGS[1] == " save") + # the second parameter may be set to save the derived parameters + isSave = true + end + + f = jldopen(sigma_k_filename, "r") + results = Any[] + for (_rs, _mass2, _F, _beta, _order) in Iterators.product(rs, mass2, Fs, beta, order) + para = ParaMC(rs=_rs, beta=_beta, Fs=_F, order=_order, mass2=_mass2, isDynamic=isDynamic, dim=dim, spin=spin) + kF = para.kF + for key in keys(f) + loadpara = ParaMC(key) + if UEG.paraid(loadpara) == UEG.paraid(para) + println(UEG.paraid(para)) + + ngrid, kgrid, rSw_k, iSw_k = UniElectronGas.getSigma(para, sigma_k_filename; parafile=parafilename) + meff, fit_p = UniElectronGas.getMeffInv(para, rSw_k, kgrid; parafile=parafilename) + # meff = UniElectronGas.getMeff(para, rSw_k, kgrid) + println("m / m* = ", meff) + push!(results, Any[_rs, _beta, _mass2, _order, meff...]) + writedlm("fit.dat", fit_p) + end + end + end + if isSave + open(inverse_meff_filename, "a+") do io + writedlm(io, results) + end + end +end diff --git a/example/sigma/derive_z.jl b/example/sigma/derive_z.jl new file mode 100644 index 0000000..662a92e --- /dev/null +++ b/example/sigma/derive_z.jl @@ -0,0 +1,33 @@ +using UniElectronGas, ElectronLiquid +using JLD2, DelimitedFiles + +include("../input.jl") + +if abspath(PROGRAM_FILE) == @__FILE__ + isSave = false + if length(ARGS) >= 1 && (ARGS[1] == "s" || ARGS[1] == "-s" || ARGS[1] == "--save" || ARGS[1] == " save") + # the second parameter may be set to save the derived parameters + isSave = true + end + + f = jldopen(sigma_k_filename, "r") + results = Any[] + for (_rs, _mass2, _F, _beta, _order) in Iterators.product(rs, mass2, Fs, beta, order) + para = ParaMC(rs=_rs, beta=_beta, Fs=_F, order=_order, mass2=_mass2, isDynamic=isDynamic, dim=dim, spin=spin) + kF = para.kF + for key in keys(f) + loadpara = ParaMC(key) + if UEG.paraid(loadpara) == UEG.paraid(para) + println(UEG.paraid(para)) + zinv = UniElectronGas.getZfactor(para; parafile=parafilename, isRenorm=false) + println("1/z = ", zinv) + push!(results, Any[_rs, _beta, _mass2, _order, zinv...]) + end + end + end + if isSave + open(zfactor_filename, "a+") do io + writedlm(io, results) + end + end +end diff --git a/example/sigma/derive_zinv.jl b/example/sigma/derive_zinv.jl new file mode 100644 index 0000000..0a68f88 --- /dev/null +++ b/example/sigma/derive_zinv.jl @@ -0,0 +1,33 @@ +using UniElectronGas, ElectronLiquid +using JLD2, DelimitedFiles + +include("../input.jl") + +if abspath(PROGRAM_FILE) == @__FILE__ + isSave = false + if length(ARGS) >= 1 && (ARGS[1] == "s" || ARGS[1] == "-s" || ARGS[1] == "--save" || ARGS[1] == " save") + # the second parameter may be set to save the derived parameters + isSave = true + end + + f = jldopen(sigma_k_filename, "r") + results = Any[] + for (_rs, _mass2, _F, _beta, _order) in Iterators.product(rs, mass2, Fs, beta, order) + para = ParaMC(rs=_rs, beta=_beta, Fs=_F, order=_order, mass2=_mass2, isDynamic=isDynamic, dim=dim, spin=spin) + kF = para.kF + for key in keys(f) + loadpara = ParaMC(key) + if UEG.paraid(loadpara) == UEG.paraid(para) + println(UEG.paraid(para)) + zinv = UniElectronGas.getZinv(para; parafile=parafilename) + println("1/z = ", zinv) + push!(results, Any[_rs, _beta, _mass2, _order, zinv...]) + end + end + end + if isSave + open(zinv_filename, "a+") do io + writedlm(io, results) + end + end +end diff --git a/example/sigma/derive_zmu.jl b/example/sigma/derive_zmu.jl index 7368e64..85f9f28 100644 --- a/example/sigma/derive_zmu.jl +++ b/example/sigma/derive_zmu.jl @@ -3,17 +3,7 @@ using JLD2, DelimitedFiles include("../input.jl") -if isLayered2D - const filename = "./data$(dim)d/data_Z_layered2d.jld2" -else - const filename = "./data$(dim)d/data_Z.jld2" -end -# const filename = "./data2d_Z_v0.jld2" -# const filename = "./data$(dim)d/data$(dim)d_Z_beta80_rs$(rs[1]).jld2" -const savefilename = spin == 2 ? "zfactor_$(dim)d.dat" : "zfactor_$(dim)d_spin$spin.dat" - - -function zfactor_renorm(dz, dzinv; isRenorm=true) +function zfactor_renorm(dz, dzinv; isRenorm=false) if isRenorm sumzinv = accumulate(+, dzinv) return @. 1.0 / (1.0 + sumzinv) @@ -24,7 +14,7 @@ function zfactor_renorm(dz, dzinv; isRenorm=true) end function process(para, datatuple, isSave) - dz, dzinv, dmu = UniElectronGas.get_dzmu(para, datatuple; parafile=parafilename, verbose=1, isSave) + dz, dzinv, dmu = UniElectronGas.get_dzmu(para, datatuple; parafile=parafilename, verbose=1, isSave=isSave) z = zfactor_renorm(dz, dzinv) println("Zfactor: ", z) @@ -38,8 +28,7 @@ if abspath(PROGRAM_FILE) == @__FILE__ isSave = true end - f = jldopen(filename, "r") - println(filename) + f = jldopen(sigma_z_filename, "r") results = Any[] for (_rs, _mass2, _F, _beta, _order) in Iterators.product(rs, mass2, Fs, beta, order) para = ParaMC(rs=_rs, beta=_beta, Fs=_F, order=_order, mass2=_mass2, isDynamic=isDynamic, dim=dim, spin=spin) @@ -54,8 +43,8 @@ if abspath(PROGRAM_FILE) == @__FILE__ end end if isSave - open(savefilename, "a+") do io + open(zfactor_filename, "a+") do io writedlm(io, results) end end -end \ No newline at end of file +end diff --git a/example/sigma/get_meff_g0w.jl b/example/sigma/get_meff_g0w.jl new file mode 100644 index 0000000..aaec4eb --- /dev/null +++ b/example/sigma/get_meff_g0w.jl @@ -0,0 +1,491 @@ +using PyCall +using PyPlot +# using Printf +using ElectronGas, ElectronLiquid, Parameters +using Lehmann, GreenFunc, CompositeGrids, CurveFit + +@pyimport numpy as np # for saving/loading numpy data +@pyimport scienceplots # for style "science" +@pyimport scipy.interpolate as interp + +# Vibrant qualitative colour scheme from https://personal.sron.nl/~pault/ +const cdict = Dict([ + "orange" => "#EE7733", + "blue" => "#0077BB", + "cyan" => "#33BBEE", + "magenta" => "#EE3377", + "red" => "#CC3311", + "teal" => "#009988", + "grey" => "#BBBBBB", +]); +style = PyPlot.matplotlib."style" +style.use(["science", "std-colors"]) +const color = [ + "black", + cdict["orange"], + cdict["blue"], + cdict["cyan"], + cdict["magenta"], + cdict["red"], + cdict["teal"], +] +rcParams = PyPlot.PyDict(PyPlot.matplotlib."rcParams") +rcParams["font.size"] = 16 +rcParams["mathtext.fontset"] = "cm" +rcParams["font.family"] = "Times New Roman" + +function spline(x, y, e; xmin=0.0, xmax=x[end]) + # generate knots with spline without constraints + w = 1.0 ./ e + spl = interp.UnivariateSpline(x, y; w=w, k=3) + __x = collect(LinRange(xmin, xmax, 1000)) + yfit = spl(__x) + return __x, yfit +end + +function get_Fs(rs) + return get_Fs_PW(rs) + # if rs < 1.0 || rs > 5.0 + # return get_Fs_DMC(rs) + # else + # return get_Fs_PW(rs) + # end +end + +""" +Get the symmetric l=0 Fermi-liquid parameter F⁰ₛ from DMC data of +Moroni, Ceperley & Senatore (1995) [Phys. Rev. Lett. 75, 689]. +""" +function get_Fs_DMC(rs) + return error("Not yet implemented!") +end + +""" +Get the symmetric l=0 Fermi-liquid parameter F⁰ₛ via interpolation of the +compressibility ratio data of Perdew & Wang (1992) [Phys. Rev. B 45, 13244]. +""" +@inline function get_Fs_PW(rs) + # if rs < 1.0 || rs > 5.0 + # @warn "The Perdew-Wang interpolation for Fs may " * + # "be inaccurate outside the metallic regime!" + # end + kappa0_over_kappa = 1.0025 - 0.1721rs - 0.0036rs^2 + # F⁰ₛ = κ₀/κ - 1 + return kappa0_over_kappa - 1.0 +end + +function get_meff_from_sigma(para::Parameter.Para; int_type=:rpa) + # Make sure we are using parameters for the bare UEG theory + @assert para.Λs == para.Λa == 0.0 + + # Small params + # kF = para.kF + # Euv, rtol = 1000 * para.EF, 1e-11 + + # Get Fermi liquid parameter F⁰ₛ(rs) from Perdew-Wang fit + rs = round(para.rs; sigdigits=13) + Fs = get_Fs(rs) + if int_type == :ko_const + println("Fermi liquid parameter at rs = $(rs): Fs = $Fs") + end + + # Get RPA+FL self-energy + sigma_tau_dynamic, sigma_tau_instant = SelfEnergy.G0W0( + para; + # Euv=Euv, + # rtol=rtol, + int_type=int_type, + Fs=int_type == :ko_const ? -Fs : nothing, # NOTE: NEFT uses opposite sign convention for F! + ) + + # Get effective mass ratio + meff, kamp = SelfEnergy.massratio(para, sigma_tau_dynamic, sigma_tau_instant) + @assert kamp ≈ para.kF + return meff +end + +# exchange interaction (Ws + Wa \sigma\sigma)_ex to a direct interaction Ws'+Wa' \sigma\sigma +# # exchange S/A interaction projected to the spin-symmetric and antisymmetric parts +function exchange2direct(Wse, Wae) + Ws = (Wse + 3 * Wae) / 2 + Wa = (Wse - Wae) / 2 + return Ws, Wa +end + +function main() + # System parameters + dim = 3 + mass2 = 1e-8 + # beta = 40.0 + beta = 1000.0 + + # rslist = [1.0, 5.0] + # rslist = [0.5, 1.0, 2.0, 3.0, 4.0, 5.0, 6.0] + # rslist = collect(LinRange(0.01, 6.0, 201)) + # rslist = collect(LinRange(0.01, 10.0, 51)) + + bigrslist = collect(LinRange(0.01, 10.0, 41)) + rslist = [0.01; collect(range(0.25, 10; step=0.25))] + rspmlist = copy(rslist) + # rspmlist = [0.5, 1.0, 2.0, 3.0, 4.0, 5.0, 6.0, 7.5, 10.0] + + # bigrslist = [0.5, 1.0, 2.0, 3.0, 4.0, 5.0, 6.0, 7.5, 10.0] + # rslist = [0.5, 1.0, 2.0, 3.0, 4.0, 5.0, 6.0, 7.5, 10.0] + + # rslist = [0.01, 1.0, 2.0, 3.0, 4.0, 5.0, 6.0] + # rslist = collect(LinRange(0.01, 6.0, 51)) + # rslist = collect(LinRange(0.01, 10.0, 11)) + + make_rs_plot = rslist != [1.0, 5.0] + make_angular_plot = rslist == [1.0, 5.0] + + # rs_Fsm1 = 5.24881 # Fs(rs ≈ 5.24881) = -1 + # rslist = [rs_Fsm1] + # make_rs_plot = false + # make_angular_plot = false + + int_type = :ko_const + # int_type = :ko_moroni + + # int_type = :ko_takada + # int_type = :ko_takada_plus + + if int_type == :ko_const + kotypestring = "const. \$f_+\$" + elseif int_type == :ko_takada + kotypestring = "Takada \$f_+\$ and \$f_-\$" + elseif int_type == :ko_takada_plus + kotypestring = "Takada \$f_+\$" + elseif int_type == :ko_moroni + kotypestring = "Moroni \$f_+\$" + end + + color = [ + [cdict["orange"], cdict["magenta"], cdict["red"]], + [cdict["blue"], cdict["cyan"], cdict["teal"]], + ] + + # Plot angular dependence and average of RPA(+FL) integrands + if make_angular_plot + fig = figure(figsize=(6, 4)) + ax = fig.add_subplot(111) + rs1_handles = [] + rs5_handles = [] + end + if make_rs_plot + F1_rpa_vs_rs = [] + F1_rpa_fl_vs_rs = [] + m_sigma_G0W0 = [] + m_sigma_G0Wp = [] + m_sigma_G0Wpm = [] + end + for (i, rs) in enumerate(bigrslist) + param = Parameter.rydbergUnit(1.0 / beta, rs) + kF, β = param.kF, param.β + + # Small params + Euv, rtol = 100 * param.EF, 1e-11 + # Euv, rtol = 1000 * param.EF, 1e-11 + + nu_grid = CompositeGrid.LogDensedGrid( + :gauss, + [-1.0, 1.0], + [-1.0, 0.0, 1.0], + 20, + 1e-6, + 12, + ) + nus = nu_grid.grid + thetas = acos.(nus) + + # |k - k'| = kF sqrt(2(1 - ν)) + k_m_kps = @. kF * sqrt(2 * (1 - nus)) + + # Get Landau parameter F⁰ₛ from Perdew & Wang compressibility fit + Fs = get_Fs(rs) + if int_type == :ko_const + println("rs = $rs, Fs = $Fs, fs = $(Fs / param.NF)") + end + + # Either use constant Fs from P&W, q-dependent Takada ansatz, or Corradini fit to Moroni DMC data + if int_type == :ko_const + landaufunc = Interaction.landauParameterConst + elseif int_type == :ko_takada + landaufunc = Interaction.landauParameterTakada + elseif int_type == :ko_takada_plus + landaufunc = Interaction.landauParameterTakadaPlus + elseif int_type == :ko_moroni + landaufunc = Interaction.landauParameterMoroni + end + + # Get W0_{+}(p, iωₙ=0) * Vinv (spin-symmetric static exchange part of RPA interaction divided by V) + W0_dyn, W0_inst = Interaction.RPAwrapped( + Euv, + rtol, + k_m_kps, + param; + regular=false, + ) + # W0_inst = 1 / V, W0_dyn = Wtilde, so W = (1 / W0_inst + W0_dyn) = V + Wtilde + W0_plus_static = @. (1 / W0_inst[1, 1, :] + W0_dyn[1, 1, :]) + + # Get R_{+}(p, iωₙ=0) * Vinv (spin-symmetric static exchange part of KO interaction divided by V) + R_dyn, R_inst = Interaction.KOwrapped( + Euv, + rtol, + k_m_kps, + param; + regular=false, + int_type=int_type, + landaufunc=landaufunc, + Fs=int_type == :ko_const ? Fs : nothing, # NOTE: NEFT uses opposite sign convention for F! + ) + # R_inst = 1 / V, R_dyn = Rtilde, so R = (1 / R_inst + R_dyn) = V + Rtilde + R_plus_static = @. (1 / R_inst[1, 1, :] + R_dyn[1, 1, :]) + + @assert maximum(imag(R_plus_static)) ≤ 1e-10 + @assert maximum(imag(W0_plus_static)) ≤ 1e-10 + + # The RPA and RPA+FL integrands are ν W0_{+}(p, iωₙ=0) and ν R_{+}(p, iωₙ=0), respectively + F1p_rpa_integrand = @. -param.NF * nus * real(W0_plus_static) + F1p_rpa_fl_integrand = @. -param.NF * nus * real(R_plus_static) + + # Perform angular integrations ν ∈ [-1, 1] + F1p_rpa = 0.5 * CompositeGrids.Interp.integrate1D(F1p_rpa_integrand / 2.0, nu_grid) + F1p_rpa_fl = 0.5 * CompositeGrids.Interp.integrate1D(F1p_rpa_fl_integrand / 2.0, nu_grid) + + # Use ElectronLiquid.jl to compute the same quantities + p_rpa = ParaMC(rs=rs, beta=beta, Fs=-0.0, order=1, mass2=mass2) + p_rpa_fl = ParaMC(rs=rs, beta=beta, Fs=-Fs, order=1, mass2=mass2) + # NOTE: NEFT uses opposite sign convention for F! + F1p_rpa_ueg, _ = -1 .* Ver4.projected_exchange_interaction(1, p_rpa, Ver4.exchange_interaction) + F1p_rpa_fl_ueg, _ = -1 .* Ver4.projected_exchange_interaction(1, p_rpa_fl, Ver4.exchange_interaction) + + println("\nrs = $rs:" * "\nF^{(RPA)+}_1 = $F1p_rpa" * "\nF^{(RPA+FL)+}_1 = $F1p_rpa_fl") + println("\nElectronLiquid:" * "\nF^{(RPA)+}_1 = $F1p_rpa_ueg" * "\nF^{(RPA+FL)+}_1 = $F1p_rpa_fl_ueg") + + if make_angular_plot + # Plot angular dependence and average of RPA integrand + plot( + thetas, + F1p_rpa .* one.(thetas); + color=color[i][1], + linestyle="--", + ) + handle_rpa, = plot( + thetas, + F1p_rpa_integrand; + color=color[i][1], + linestyle="-", + label="RPA", + ) + # Plot angular dependence and average of RPA integrand + plot( + thetas, + F1p_rpa_fl .* one.(thetas); + color=color[i][2], + linestyle="--", + ) + handle_rpa_fl, = plot( + thetas, + F1p_rpa_fl_integrand; + color=color[i][2], + linestyle="-", + label="\$G_{+}\$", + # label="\$G_{+},\\; $kotypestring\$", + ) + handles = [handle_rpa, handle_rpa_fl] + if rs == 1 + append!(rs1_handles, handles) + elseif rs == 5 + append!(rs5_handles, handles) + end + end + if make_rs_plot + push!(F1_rpa_vs_rs, F1p_rpa) + push!(F1_rpa_fl_vs_rs, F1p_rpa_fl) + end + end + for (i, rs) in enumerate(rspmlist) + param = Parameter.rydbergUnit(1.0 / beta, rs) + m_sigma_G0Wpm_this_rs = get_meff_from_sigma(param; int_type=:ko_simion_giuliani) + # m_sigma_G0Wpm_this_rs = get_meff_from_sigma(param; int_type=:ko_takada) + + if make_rs_plot + push!(m_sigma_G0Wpm, m_sigma_G0Wpm_this_rs) + end + end + for (i, rs) in enumerate(rslist) + param = Parameter.rydbergUnit(1.0 / beta, rs) + m_sigma_G0W0_this_rs = get_meff_from_sigma(param; int_type=:rpa) + m_sigma_G0Wp_this_rs = get_meff_from_sigma(param; int_type=:ko_moroni) + # m_sigma_G0Wpm_this_rs = get_meff_from_sigma(param; int_type=:ko_takada) + + # m_sigma_G0Wp_this_rs = get_meff_from_sigma(param; int_type=:ko_const) + + # m_sigma_G0Wp_this_rs = get_meff_from_sigma(param; int_type=:ko_takada_plus) + # m_sigma_G0Wpm_this_rs = get_meff_from_sigma(param; int_type=:ko_takada) + + if make_rs_plot + push!(m_sigma_G0W0, m_sigma_G0W0_this_rs) + push!(m_sigma_G0Wp, m_sigma_G0Wp_this_rs) + # push!(m_sigma_G0Wpm, m_sigma_G0Wpm_this_rs) + end + end + if make_angular_plot + xticks([0, π / 4, π / 2, 3π / 4, π], ["\$0\$", "\$\\pi/4\$", "\$\\pi/2\$", "\$3\\pi/4\$", "\$\\pi\$"]) + xlim(0, π) + xlabel("\$\\theta\$") + ylabel("\$P_1(\\cos\\theta) F^+_{1,1}(\\theta)\$") + + # Assemble legends + top_legend = plt.legend(handles=rs1_handles, loc=(0.5, 0.325), fontsize=14, title="\$r_s = 1\$", ncol=2, columnspacing=0.9) + bottom_legend = plt.legend(handles=rs5_handles, loc=(0.5, 0.09), fontsize=14, title="\$r_s = 5\$", ncol=2, columnspacing=0.9) + ax.add_artist(top_legend) + ax.add_artist(bottom_legend) + tight_layout() + savefig("Fp1_rpa_and_rpa_fl_angular_dependence_$(int_type).pdf") + end + if make_rs_plot + # Plot F1 vs rs + # fig2 = figure(figsize=(5, 5)) + fig2 = figure(figsize=(6, 6)) + ax2 = fig2.add_subplot(111) + + function plot_mvsrs(rs, meff_data, color, label, ls="-", ax=ax2; rs_HDL=nothing, meff_HDL=nothing, zorder=nothing) + # Add data in the high-density limit to the fit, if provided + if !isnothing(rs_HDL) && !isnothing(meff_HDL) + _rslist = unique([rs; rs_HDL]) + mdatalist = unique([meff_data; meff_HDL]) + P = sortperm(_rslist) + rs = _rslist[P] + meff_data = mdatalist[P] + end + + # mfitfunc = interp.PchipInterpolator(rs, meff_data) + mfitfunc = interp.Akima1DInterpolator(rs, meff_data) + xgrid = np.arange(0, maximum(_rslist) + 0.2, 0.01) + # xgrid = np.arange(0, 6.2, 0.01) + # ax.scatter(rs, meff_data; color=color, marker="o") + if isnothing(zorder) + handle, = ax.plot(xgrid, mfitfunc(xgrid), ls=ls, color=color, label=label) + else + handle, = ax.plot(xgrid, mfitfunc(xgrid), ls=ls, color=color, label=label, zorder=zorder) + end + yfit = np.ma.masked_invalid(mfitfunc(xgrid)) + # print(yfit) + # print("Turning point: rs = ", xgrid[np.argmin(yfit)]) + # print("Effective mass ratio at turning point: ", np.min(yfit)) + return handle + end + + # Taylor series for m* / m in the high-density limit to leading order in rs + # (c.f. Giuliani & Vignale, Quantum Theory of the Electron Liquid, 2008, p. 500) + function high_density_limit(x) + alpha = (4 / 9π)^(1 / 3.0) + return 1 + alpha * x * log(x) / 2π + end + + # High-density limit + rs_HDL_plot = collect(LinRange(1e-5, 0.35, 101)) + meff_HDL_plot = high_density_limit.(rs_HDL_plot) + + # Use exact expression in the high-density limit for RPT and Simion & Giuliani fits + cutoff_HDL = 0.1 + rs_HDL = rs_HDL_plot[rs_HDL_plot.≤cutoff_HDL] + meff_HDL = meff_HDL_plot[rs_HDL_plot.≤cutoff_HDL] + println(rs_HDL) + println(meff_HDL) + + # Add points at rs = 0 + pushfirst!(bigrslist, 0.0) + pushfirst!(rslist, 0.0) + pushfirst!(rspmlist, 0.0) + pushfirst!(rs_HDL, 0.0) + pushfirst!(meff_HDL, 1.0) + pushfirst!(rs_HDL_plot, 0.0) + pushfirst!(meff_HDL_plot, 1.0) + pushfirst!(F1_rpa_vs_rs, 0.0) + pushfirst!(F1_rpa_fl_vs_rs, 0.0) + pushfirst!(m_sigma_G0W0, 1.0) + pushfirst!(m_sigma_G0Wp, 1.0) + pushfirst!(m_sigma_G0Wpm, 1.0) + + # Save data + np.savez("m_sigma_G0W0", rslist=rslist, mefflist=m_sigma_G0W0) + # np.savez("m_sigma_G0Wp", rslist=rslist, mefflist=m_sigma_G0Wp) + # np.savez("m_sigma_G0Wpm", rslist=rspmlist, mefflist=m_sigma_G0Wpm) + np.savez("m_tree_level_G0W0", rslist=bigrslist, mefflist=(1 .+ F1_rpa_vs_rs)) + np.savez("m_tree_level_G0Wp", rslist=bigrslist, mefflist=(1 .+ F1_rpa_fl_vs_rs)) + + colors = [ + cdict["orange"], + cdict["blue"], + cdict["magenta"], + cdict["cyan"], + cdict["red"], + cdict["teal"], + "black", + ] + + # High-density limit + # plot_mvsrs(rs_HDL_plot, meff_HDL_plot, colors[1], "High-density limit", "--"; zorder=1000) + + # Tree-level RPA + plot_mvsrs(bigrslist, 1 .+ F1_rpa_vs_rs, "black", "Tree-level \$F^+_1\$, \$G_0 W_0\$", "--"; rs_HDL=rs_HDL, meff_HDL=meff_HDL) + + # Tree-level RPA+FL + plot_mvsrs(bigrslist, 1 .+ F1_rpa_fl_vs_rs, "black", "Tree-level \$F^+_1\$, \$G_0 W_+\$", ":"; rs_HDL=rs_HDL, meff_HDL=meff_HDL) + + println() + println(bigrslist) + println() + println(rslist) + + # Self-energy G_0 W_0 + plot_mvsrs(rslist, m_sigma_G0W0, colors[1], "\$G_0 W_0\$"; rs_HDL=rs_HDL, meff_HDL=meff_HDL) + + # Self-energy G_0 W_+ (Moroni) + plot_mvsrs(rslist, m_sigma_G0Wp, colors[2], "\$G_0 W_+\$"; rs_HDL=rs_HDL, meff_HDL=meff_HDL) + + # Self-energy G_0 W_± (Simion & Giuliani) + plot_mvsrs(rspmlist, m_sigma_G0Wpm, colors[3], "\$G_0 W_\\pm\$"; rs_HDL=rs_HDL, meff_HDL=meff_HDL) + # ax2.scatter(rspmlist, m_sigma_G0Wpm; color=colors[3], marker="v", zorder=600) + + # Simion & Giuliani self-energy G_0 W_0, G_0 W_+, and G_0 W_± results + rs_RPA = [0, 1, 2, 3, 4, 5, 6] + m_G0W0 = [1.0, 0.970, 0.992, 1.016, 1.039, 1.059, 1.078] + m_Gp = [1.0, 0.952, 0.951, 0.956, 0.962, 0.968, 0.973] + m_Gpm = [1.0, 0.957, 0.966, 0.983, 1.005, 1.028, 1.055] + # plot_mvsrs(rs_RPA, m_G0W0, "black", "\$\\Sigma_{G_0 W_0}\$", ":") + # plot_mvsrs(rs_RPA, m_Gp, "black", "\$\\Sigma_{G_0 W_+}\$", "-.") + # plot_mvsrs(rs_RPA, m_G0W0, colors[5], "\$\\Sigma_{G_0 W_0}\$ (Simion, 2008)", "--"; rs_HDL=rs_HDL, meff_HDL=meff_HDL) + # plot_mvsrs(rs_RPA, m_Gp, colors[6], "\$\\Sigma_{G_0 W_+}\$ (Simion, 2008)", "--"; rs_HDL=rs_HDL, meff_HDL=meff_HDL) + # plot_mvsrs(rs_RPA, m_Gpm, "black", "\$\\Sigma_{G_0 W_\\pm}\$", "--"; rs_HDL=rs_HDL, meff_HDL=meff_HDL) + ax2.scatter(rs_RPA, m_G0W0; color=colors[4], marker="^", label="\$G_0 W_0\$ (Ref. [16])", zorder=700) + ax2.scatter(rs_RPA, m_Gp; color=colors[5], marker="s", label="\$G_0 W_+\$ (Ref. [16])", zorder=800) + ax2.scatter(rs_RPA, m_Gpm; color=colors[6], marker="D", label="\$G_0 W_\\pm\$ (Ref. [16])", zorder=900) + + # RPT Monte Carlo results for full m* / m + m_VDMC = [1.0, 0.95893, 0.9514, 0.9516, 0.9597, 0.9692, 0.9771, 0.9842] + m_VDMC_err = [0, 0.00067, 0.0016, 0.0018, 0.0016, 0.0026, 0.0028, 0.0029] + rs_VDMC = [0, 0.5, 1, 2, 3, 4, 5, 6] + ax2.errorbar(rs_VDMC, m_VDMC, m_VDMC_err; fmt="o", capthick=1, capsize=4, ms=5, color="black", label="RPT (This work)", zorder=1000) + plot_mvsrs(rs_VDMC, m_VDMC, "black", nothing; rs_HDL=rs_HDL, meff_HDL=meff_HDL) + + legend(loc="best", fontsize=12) + # legend(loc="best", ncol=2, columnspacing=0.45, fontsize=10) + # legend(loc="best", ncol=2, columnspacing=0.45) + # legend(loc=(0.09, 0.625)) + # legend(loc=(0.1, 0.5)) + ylabel("\$m^*/m\$") + xlabel("\$r_s\$") + # ylim(0.94, 1.02) + tight_layout() + savefig("effective_mass_comparisons.pdf") + # savefig("meff3d_tree_level.pdf") + # savefig("Fp1_rpa_and_rpa_fl_vs_rs_$(int_type).pdf") + end +end + +main() diff --git a/example/sigma/get_meff_gw.jl b/example/sigma/get_meff_gw.jl new file mode 100644 index 0000000..485029b --- /dev/null +++ b/example/sigma/get_meff_gw.jl @@ -0,0 +1,405 @@ +using CompositeGrids +using ElectronGas +using ElectronLiquid +using JLD2 +using PyCall + +@pyimport numpy as np # for saving/loading numpy data + +@inline function get_Fs(rs) + return get_Fs_PW(rs) + # if rs < 1.0 || rs > 5.0 + # return get_Fs_DMC(rs) + # else + # return get_Fs_PW(rs) + # end +end + +""" +Get the symmetric l=0 Fermi-liquid parameter F⁰ₛ from DMC data of +Moroni, Ceperley & Senatore (1995) [Phys. Rev. Lett. 75, 689]. +""" +@inline function get_Fs_DMC(rs) + return error("Not yet implemented!") +end + +""" +Get the symmetric l=0 Fermi-liquid parameter F⁰ₛ via interpolation of the +compressibility ratio data of Perdew & Wang (1992) [Phys. Rev. B 45, 13244]. +""" +@inline function get_Fs_PW(rs) + # if rs < 1.0 || rs > 5.0 + # @warn "The Perdew-Wang interpolation for Fs may " * + # "be inaccurate outside the metallic regime!" + # end + kappa0_over_kappa = 1.0025 - 0.1721rs - 0.0036rs^2 + # F⁰ₛ = κ₀/κ - 1 + return kappa0_over_kappa - 1.0 +end + +""" +Get the antisymmetric l=0 Fermi-liquid parameter F⁰ₐ via interpolation of the +susceptibility ratio data (c.f. Kukkonen & Chen, 2021) +""" +@inline function get_Fa(rs) + chi0_over_chi = 0.9821 - 0.1232rs + 0.0091rs^2 + # F⁰ₐ = χ₀/χ - 1 + return chi0_over_chi - 1.0 +end + +function GW0(G_prev, param, Euv, rtol, Nk, maxK, minK, order, int_type, kgrid::Union{AbstractGrid,AbstractVector,Nothing}=nothing; kwargs...) + dim = param.dim + + if dim == 2 + if isnothing(kgrid) + kernel = SelfEnergy.LegendreInteraction.DCKernel_2d(param; + Euv=Euv, rtol=rtol, Nk=Nk, maxK=maxK, minK=minK, order=order, int_type=int_type, spin_state=:sigma, kwargs...) + else + if (kgrid isa AbstractVector) + kgrid = SimpleG.Arbitrary{eltype(kgrid)}(kgrid) + end + kernel = SelfEnergy.LegendreInteraction.DCKernel_2d(param; + Euv=Euv, rtol=rtol, Nk=Nk, maxK=maxK, minK=minK, order=order, int_type=int_type, spin_state=:sigma, kgrid=kgrid, kwargs...) + end + Σ, Σ_ins = SelfEnergy.calcΣ_2d(G_prev, kernel) + elseif dim == 3 + if isnothing(kgrid) + kernel = SelfEnergy.LegendreInteraction.DCKernel0(param; + Euv=Euv, rtol=rtol, Nk=Nk, maxK=maxK, minK=minK, order=order, int_type=int_type, spin_state=:sigma, kwargs...) + else + if (kgrid isa AbstractVector) + kgrid = SimpleG.Arbitrary{eltype(kgrid)}(kgrid) + end + kernel = SelfEnergy.LegendreInteraction.DCKernel0(param; + Euv=Euv, rtol=rtol, Nk=Nk, maxK=maxK, minK=minK, order=order, int_type=int_type, spin_state=:sigma, kgrid=kgrid, kwargs...) + end + Σ, Σ_ins = SelfEnergy.calcΣ_3d(G_prev, kernel) + else + error("No support for G0W0 in $dim dimension!") + end + + return Σ, Σ_ins +end + +function GW0(G_prev, param, kgrid::Union{AbstractGrid,AbstractVector,Nothing}=nothing; Euv=100 * param.EF, atol=1e-14, Nk=12, maxK=6 * param.kF, minK=1e-8 * param.kF, order=8, int_type=:rpa, kwargs...) + return GW0(G_prev, param, Euv, atol, Nk, maxK, minK, order, int_type, kgrid; kwargs...) +end + +function get_meff_from_Σ_GW(param::Parameter.Para; int_type=:rpa, δK=5e-6, max_steps=10, atol=1e-7, alpha=0.3, save_sigma=false) + # Get RPA+FL self-energy + Σ_tau_dynamic, Σ_tau_instant = get_Σ_GW(param, int_type, max_steps, atol, alpha, δK, save_sigma) + + # Get effective mass ratio + meff, kamp = SelfEnergy.massratio(param, Σ_tau_dynamic, Σ_tau_instant, δK) + @assert kamp ≈ param.kF + return meff +end + +# Helper function for linear interpolation with mixing parameter α +function LERP(M_start, M_end, alpha) + return (1 - alpha) * M_start + alpha * M_end +end + +function get_Σ_GW(param::Parameter.Para, int_type, max_steps, atol, alpha, δK, save_sigma) + # Make sigma output directory if needed + if save_sigma + mkpath("results/sigma_GW_$(param.dim)d") + dir = joinpath(@__DIR__, "results/sigma_GW_$(param.dim)d") + end + + # Make sure we are using parameters for the bare UEG theory + @assert param.Λs == param.Λa == 0.0 + + # Get Fermi liquid parameter F⁰ₛ(rs) from Perdew-Wang fit + rs = round(param.rs; sigdigits=13) + Fs = get_Fs(rs) + Fa = get_Fa(rs) + if int_type in [:ko_const_p, :ko_const_pm] + _int_type = :ko_const + if int_type == :ko_const_pm + println("Fermi liquid parameters at rs = $(rs): Fs = $Fs, Fa = $Fa") + end + else + _int_type = int_type + end + + # DLR cutoffs + kF = param.kF + Euv, rtol_dlr = 1000 * param.EF, 1e-11 + maxK, minK = 20kF, 1e-8kF + Nk, order = 12, 8 + + # Helper function to get the GW self-energy Σ[G, W] for a given int_type (W) + # NOTE: A large momentum grid is required for G and Σ at intermediate steps + function Σ_GW0(G) + return GW0( + G, + param; + # kgrid; + Euv=Euv, + rtol=rtol_dlr, + Nk=Nk, + maxK=maxK, + minK=minK, + order=order, + int_type=_int_type, + Fs=_int_type == :ko_const ? -Fs : -0.0, # NOTE: NEFT uses opposite sign convention for F! + Fa=int_type == :ko_const_pm ? -Fa : -0.0, # NOTE: NEFT uses opposite sign convention for F! + ) + end + + # G0 for the UEG; a large kgrid is required for the self-consistency loop + kgrid = CompositeGrid.LogDensedGrid(:cheb, [0.0, maxK], [0.0, param.kF], Nk, minK, order) + G0 = SelfEnergy.G0wrapped(Euv, rtol_dlr, kgrid, param) + + # Initial G0W self-energy: Σ[G0, W] + Σ, Σ_ins = Σ_GW0(G0) + G_prev = G0 + δμ_prev = SelfEnergy.chemicalpotential(param, Σ, Σ_ins) + meff_prev, kamp = SelfEnergy.massratio(param, Σ, Σ_ins, δK) + zfactor_prev = SelfEnergy.zfactor(param, Σ; ngrid=[-1, 0])[1] + @assert kamp ≈ param.kF + + # Write initial (G0W0) self-energy to JLD2 file, overwriting if it already exists + if save_sigma + jldopen(joinpath(dir, "sigma_$(int_type)_rs$(rs).jl"), "w") do file + file["Σ_0"] = Σ + file["Σ_ins_0"] = Σ_ins + end + end + + # Self-consistency loop for G + println("\nBegin self-consistency loop...\n") + i_step = 0 + while i_step < max_steps + δμ = SelfEnergy.chemicalpotential(param, Σ, Σ_ins) + meff = SelfEnergy.massratio(param, Σ, Σ_ins, δK)[1] + zfactor = SelfEnergy.zfactor(param, Σ; ngrid=[-1, 0])[1] + + print("""\n + Step $(i_step + 1): + • m*/m = \t$(meff) + • Z = \t$(zfactor) + • δμ = \t$(δμ) + """) + + # Use Dyson's equation to find G = 1 / (G0⁻¹ - Σ) + # NOTE: Σ and Σ_ins are converted to the Matsubara representation internally + G = SelfEnergy.Gwrapped(Σ, Σ_ins, param) + + # Get Σ[G_mix, W], where the input Green's function is a linear interpolation + # of the previous and current G: G_mix = (1 - α) * G_prev + α * G + G_mix = LERP(G_prev, G, alpha) + Σ, Σ_ins = Σ_GW0(G_mix) + + # Append self-energy at this step to JLD2 file + if save_sigma + jldopen(joinpath(dir, "sigma_$(int_type)_rs$(rs).jl"), "a+") do file + file["Σ_$(i_step + 1)"] = Σ + file["Σ_ins_$(i_step + 1)"] = Σ_ins + end + end + + # Test for convergence of quasiparticle properties + if i_step > 0 + dmeff = abs(meff - meff_prev) + dzfactor = abs(zfactor - zfactor_prev) + ddeltamu = abs(δμ - δμ_prev) + print(""" + • |Δ(m* / m)| = \t$(dmeff) + • |Δ(Z)| = \t$(dzfactor) + • |Δ(δμ)| = \t$(ddeltamu) + """) + if all([dmeff, dzfactor, ddeltamu] .< atol) + println("\nConverged to atol = $atol after $i_step steps!") + break + end + end + + # Prepare for next iteration + i_step += 1 + # G_prev = G + G_prev = G_mix + δμ_prev = δμ + meff_prev = meff + zfactor_prev = zfactor + end + if i_step == max_steps + println("\nWARNING: Convergence to atol = $atol not reached after $max_steps steps!") + end + return Σ, Σ_ins +end + +function get_meff_from_Σ_G0W(param::Parameter.Para; δK=5e-6, int_type=:rpa) + # Make sure we are using parameters for the bare UEG theory + @assert param.Λs == param.Λa == 0.0 + + # DLR cutoffs + kF = param.kF + Euv, rtol_dlr = 1000 * param.EF, 1e-11 + maxK, minK = 20kF, 1e-8kF + Nk, order = 12, 8 + + # Get Fermi liquid parameter F⁰ₛ(rs) from Perdew-Wang fit + rs = round(param.rs; sigdigits=13) + Fs = get_Fs(rs) + Fa = get_Fa(rs) + if int_type in [:ko_const_p, :ko_const_pm] + _int_type = :ko_const + if int_type == :ko_const_pm + println("Fermi liquid parameters at rs = $(rs): Fs = $Fs, Fa = $Fa") + end + else + _int_type = int_type + end + + # Get RPA+FL self-energy + Σ_tau_dynamic, Σ_tau_instant = SelfEnergy.G0W0( + param; + # kgrid; + Euv=Euv, + rtol=rtol_dlr, + Nk=Nk, + maxK=maxK, + minK=minK, + order=order, + int_type=_int_type, + Fs=_int_type == :ko_const ? -Fs : -0.0, # NOTE: NEFT uses opposite sign convention for F! + Fa=int_type == :ko_const_pm ? -Fa : -0.0, # NOTE: NEFT uses opposite sign convention for F! + ) + + # Get effective mass ratio + meff, kamp = SelfEnergy.massratio(param, Σ_tau_dynamic, Σ_tau_instant, δK) + @assert kamp ≈ param.kF + return meff +end + +function main() + # System parameters + dim = 3 + beta = 1000.0 + δK = 5e-6 + # GW parameters + max_steps = 100 + atol = 1e-7 + alpha = 0.3 + + calc_g0w = false + calc_gw = true + save_sigma = true + + # Output directory + mkpath("results/finalized_meff_results/$(dim)d") + dir = joinpath(@__DIR__, "results/finalized_meff_results/$(dim)d") + + # rslist = [0.001; collect(LinRange(0.0, 1.1, 111))[2:end]] # for accurate 2D HDL + # rslist = [0.005; collect(LinRange(0.0, 5.0, 101))[2:end]] # for 2D + # rslist = [0.01; collect(LinRange(0.0, 10.0, 101))[2:end]] # for 3D + + # rslist = [0.001; collect(range(0.0, 1.1, step=0.05))[2:end]] # for accurate 2D HDL + rslist = [0.01; collect(range(0.0, 10.0, step=0.5))[2:end]] # for 3D + # rslist = [1.0, 3.0] + + # NOTE: int_type ∈ [:ko_const, :ko_takada_plus, :ko_takada, :ko_moroni, :ko_simion_giuliani] + # NOTE: KO interaction using G+ and/or G- is currently only available in 3D + # int_type_Gp = :ko_const_p + # int_type_Gpm = :ko_const_pm + int_type_Gp = :ko_moroni + int_type_Gpm = :ko_simion_giuliani + @assert int_type_Gp ∈ [:ko_const_p, :ko_takada_plus, :ko_moroni] + @assert int_type_Gpm ∈ [:ko_const_pm, :ko_takada, :ko_simion_giuliani] + + if int_type_Gpm == :ko_const_pm + ko_dirstr = "const" + elseif int_type_Gpm == :ko_takada + ko_dirstr = "takada" + elseif int_type_Gpm == :ko_simion_giuliani + ko_dirstr = "simion_giuliani" + end + + # G0W effective masses + if calc_g0w + m_Σ_G0W0 = [] + if dim == 3 + m_Σ_G0Wp = [] + m_Σ_G0Wpm = [] + end + for rs in rslist + param = Parameter.rydbergUnit(1.0 / beta, rs, dim) + + print("Calculating m*/m[G0W] values for rs = $rs...") + m_Σ_G0W0_this_rs = get_meff_from_Σ_G0W(param; δK=δK, int_type=:rpa) + if dim == 3 + m_Σ_G0Wp_this_rs = get_meff_from_Σ_G0W(param; δK=δK, int_type=int_type_Gp) + m_Σ_G0Wpm_this_rs = get_meff_from_Σ_G0W(param; δK=δK, int_type=int_type_Gpm) + end + println("done.") + + push!(m_Σ_G0W0, m_Σ_G0W0_this_rs) + if dim == 3 + push!(m_Σ_G0Wp, m_Σ_G0Wp_this_rs) + push!(m_Σ_G0Wpm, m_Σ_G0Wpm_this_rs) + end + end + # Add points at rs = 0 + pushfirst!(rslist, 0.0) + pushfirst!(m_Σ_G0W0, 1.0) + if dim == 3 + pushfirst!(m_Σ_G0Wp, 1.0) + pushfirst!(m_Σ_G0Wpm, 1.0) + end + # Save data + np.savez(joinpath(dir, "rpa/meff_$(dim)d_sigma_G0W0.npz"), rslist=rslist, mefflist=m_Σ_G0W0) + if dim == 3 + np.savez(joinpath(dir, "$(ko_dirstr)/meff_$(dim)d_sigma_G0Wp.npz"), rslist=rslist, mefflist=m_Σ_G0Wp) + np.savez(joinpath(dir, "$(ko_dirstr)/meff_$(dim)d_sigma_G0Wpm.npz"), rslist=rslist, mefflist=m_Σ_G0Wpm) + end + end + + # GW effective masses + if calc_gw + # m_Σ_GW0 = [] + if dim == 3 + m_Σ_GWp = [] + m_Σ_GWpm = [] + end + _rslist = calc_g0w ? rslist[2:end] : rslist + for rs in _rslist + param = Parameter.rydbergUnit(1.0 / beta, rs, dim) + + print("Calculating m*/m[GW] values for rs = $rs...") + # m_Σ_GW0_this_rs = get_meff_from_Σ_GW(param; int_type=:rpa, δK=δK, + # max_steps=max_steps, atol=atol, alpha=alpha, save_sigma=save_sigma) + if dim == 3 + m_Σ_GWp_this_rs = get_meff_from_Σ_GW(param; int_type=int_type_Gp, δK=δK, + max_steps=max_steps, atol=atol, alpha=alpha) + m_Σ_GWpm_this_rs = get_meff_from_Σ_GW(param; int_type=int_type_Gpm, δK=δK, + max_steps=max_steps, atol=atol, alpha=alpha) + end + println("done.") + + # push!(m_Σ_GW0, m_Σ_GW0_this_rs) + if dim == 3 + push!(m_Σ_GWp, m_Σ_GWp_this_rs) + push!(m_Σ_GWpm, m_Σ_GWpm_this_rs) + end + end + # Add points at rs = 0 + if calc_g0w == false + pushfirst!(rslist, 0.0) + end + # pushfirst!(m_Σ_GW0, 1.0) + if dim == 3 + pushfirst!(m_Σ_GWp, 1.0) + pushfirst!(m_Σ_GWpm, 1.0) + end + # Save data + # np.savez(joinpath(dir, "rpa/meff_$(dim)d_sigma_GW0.npz"), rslist=rslist, mefflist=m_Σ_GW0) + if dim == 3 + np.savez(joinpath(dir, "$(ko_dirstr)/meff_$(dim)d_sigma_GWp.npz"), rslist=rslist, mefflist=m_Σ_GWp) + np.savez(joinpath(dir, "$(ko_dirstr)/meff_$(dim)d_sigma_GWpm.npz"), rslist=rslist, mefflist=m_Σ_GWpm) + end + end +end + +main() diff --git a/example/sigma/plot_meff.jl b/example/sigma/plot_meff.jl deleted file mode 100644 index 676ccec..0000000 --- a/example/sigma/plot_meff.jl +++ /dev/null @@ -1,183 +0,0 @@ -using PyPlot, PyCall -using DelimitedFiles -using CurveFit - -# @pyimport scienceplots # `import scienceplots` is required as of version 2.0.0 -@pyimport scipy.interpolate as interp - -dim = 2 -# spin = 2 -spin = 1 -# rs = [0.5, 1.0, 4.0] -# rs = [0.5] -rs = [1.0] -# mass2 = [1.0, 1.5, 2.0, 2.5, 3.0, 3.5, 4.0, 4.5, 5.0] -mass2 = [0.5, 0.75, 1.0, 1.25, 1.5, 1.75, 2.0, 2.2, 2.4, 2.5, 2.6, 2.8, 3.0, 3.5, 4.0, 4.5, 5.0, 5.5, 6.0, 7.0, 8.0] -# mass2 = [1.5, 2.0, 2.2, 2.4, 2.5, 2.6, 2.8, 3.0, 3.5, 4.0, 4.5, 5.0, 6.0, 7.0, 8.0] -Fs = [-0.0,] -beta = [25.0] -order = [4,] -# order = [5,] -const fileName = spin == 2 ? "meff_$(dim)d.dat" : "meff_$(dim)d_spin$spin.dat" - -cdict = Dict(["blue" => "#0077BB", "cyan" => "#33BBEE", "teal" => "#009988", "orange" => "#EE7733", "red" => "#CC3311", "magenta" => "#EE3377", "grey" => "#BBBBBB"]); - -function spline(x, y, e; xmin=x[1], xmax=x[end]) - # generate knots with spline without constraints - w = 1.0 ./ e - spl = interp.UnivariateSpline(x, y; w=w, k=3) - __x = collect(LinRange(xmin, xmax, 100)) - yfit = spl(__x) - return __x, yfit -end - -function plot_convergence(meff, errors, _mass2=mass2, maxOrder=order[1]; rs=rs[1], beta=beta[1]) - style = PyPlot.matplotlib."style" - style.use(["science", "std-colors"]) - color = [cdict["blue"], cdict["red"], cdict["teal"], cdict["orange"], "black", cdict["cyan"], cdict["grey"]] - #cmap = get_cmap("Paired") - rcParams = PyPlot.PyDict(PyPlot.matplotlib."rcParams") - rcParams["font.size"] = 16 - rcParams["font.family"] = "Times New Roman" - figure(figsize=(6, 4)) - - x = collect(1:maxOrder) - for (idx, yval) in enumerate(meff) - yerr = errors[idx] - errorbar(x, yval, yerr=yerr, color=color[idx], capsize=4, fmt="o", markerfacecolor="none", label="\$N=\$ $(_mass2[idx])") - end - # xlim(0.8, 4.5) - xlabel("Order") - ylabel("\$m^*/m\$") - legend(title="mass2") - # title("rs=$rs, beta=$beta") - title("rs=$rs") - savefig("meff$(dim)d_rs$(rs)_beta$(beta)_spin1_conv_fitted.pdf") -end - -function plot_convergence_v1(meff, errors, _mass2=mass2, maxOrder=order[1]; rs=rs[1], beta=beta[1]) - style = PyPlot.matplotlib."style" - style.use(["science", "std-colors"]) - # color = [cdict["blue"], cdict["red"], cdict["teal"], cdict["orange"], cdict["cyan"], cdict["magenta"], cdict["grey"], "black"] - color = [cdict["blue"], cdict["red"], cdict["teal"], cdict["orange"], "black", cdict["cyan"], cdict["grey"]] - #cmap = get_cmap("Paired") - rcParams = PyPlot.PyDict(PyPlot.matplotlib."rcParams") - rcParams["font.size"] = 16 - rcParams["font.family"] = "Times New Roman" - figure(figsize=(6, 4)) - - x = _mass2 - xgrid = LinRange(0.5, 5.5, 100) - for o in 1:maxOrder - yval, yerr = meff[o], errors[o] - println("Order $o: ", x, yval, yerr) - errorbar(x, yval, yerr=yerr, color=color[o], capsize=4, fmt="o", markerfacecolor="none", label="\$N=\$ $o") - - # yfit = curve_fit(Polynomial, x, yval, 4) - if o < 5 - xfit, yfit = spline(x, yval, yerr) - # plot(xgrid, yfit.(xgrid), color=color[o]) - plot(xfit, yfit, color=color[o]) - end - end - mres = zeros(3) - - legend_loc = 4 - if spin == 2 - if rs == 0.1 - mres = [0.9665, 0.9675, 0.9685] - xlim(0.8, 5.2) #rs=0.1 - ylim(0.961, 0.975) - elseif rs == 0.3 - mres = [0.95, 0.951, 0.952] - xlim(0.8, 5.2) #rs=0.3 - ylim(0.937, 0.961) - elseif rs == 0.5 - mres = [0.9495, 0.952, 0.9545] - xlim(0.8, 4.7) #rs=0.5 - ylim(0.94, 0.98) - legend_loc = 2 - elseif rs == 1.0 - mres = [0.966, 0.97, 0.974] - xlim(0.8, 5.2) #rs=1 - ylim(0.945, 0.992) - # ylim(0.88, 1.0) - end - elseif spin == 1 - xlim(0.4, 2.1) - ylim(0.8, 0.9) - end - # axhspan(mres[1], mres[3], color=cdict["cyan"], alpha=0.5) - # plot([0, 6], [mres[2], mres[2]], color="black", ls="--") - - xlabel("\$\\lambda\$ (Ry)") - ylabel("\$m^*/m\$") - # legend(title="order", loc=2) - # legend(title="order", loc=4) - legend(fontsize=12, loc=legend_loc) - # title("rs=$rs, beta=$beta") - title("\$r_s=\$ $rs") - if spin == 2 - savefig("meff$(dim)d_rs$(rs)_beta$(beta)_conv1.pdf") - else - savefig("meff$(dim)d_rs$(rs)_beta$(beta)_spin$(spin)_conv1.pdf") - end -end - -if abspath(PROGRAM_FILE) == @__FILE__ - - meff_data = readdlm(fileName) - num_data = size(meff_data)[1] - # num_data = 8 - - # mass2_all = meff_data[:, 3] - # meff_order, error_order = [], [] - # for o in 1:4 - # push!(meff_order, meff_data[:, 3o+2]) - # push!(error_order, meff_data[:, 3o+4]) - # end - - for _rs in rs - meff_total, error_total, mass2_total = [], [], [] - # for (_rs, _beta, _mass2) in Iterators.product(rs, beta, mass2) - for (_beta, _mass2) in Iterators.product(beta, mass2) - idx = 0 - # println(_rs, _beta, _mass2) - for i in 1:num_data - # if meff_data[i, 1:3] == [_rs, _beta, _mass2] - if meff_data[i, 1] == _rs && meff_data[i, 3] == _mass2 - idx = i - break - end - end - idx == 0 && continue - _order = meff_data[idx, 4] - meff, error = [], [], [] - for o in 1:_order - push!(meff, meff_data[idx, 3o+2]) - push!(error, meff_data[idx, 3o+4]) - end - if _order < order[1] - push!(meff, 0.0) - push!(error, 0.0) - end - push!(meff_total, meff) - push!(error_total, error) - push!(mass2_total, meff_data[idx, 3]) - end - println(meff_total) - println(error_total) - println(mass2_total) - # plot_convergence(meff_total, error_total, mass2_total) - - meff_total = hcat(meff_total...) - error_total = hcat(error_total...) - meff_order, error_order = [], [] - for o in 1:order[1] - push!(meff_order, meff_total[o, :]) - push!(error_order, error_total[o, :]) - end - - plot_convergence_v1(meff_order, error_order, mass2_total, rs=_rs) - end -end \ No newline at end of file diff --git a/example/sigma/plot_meff2d.py b/example/sigma/plot_meff2d.py new file mode 100644 index 0000000..5459c3a --- /dev/null +++ b/example/sigma/plot_meff2d.py @@ -0,0 +1,225 @@ +#!/usr/bin/python3 +import scienceplots +import numpy as np +import pandas as pd +from scipy import interpolate +import matplotlib as mat +import matplotlib.pyplot as plt +from mpl_toolkits.axes_grid1.inset_locator import inset_axes + +cdict = { + "blue": "#0077BB", + "cyan": "#33BBEE", + "teal": "#009988", + "orange": "#EE7733", + "red": "#CC3311", + "magenta": "#EE3377", + "grey": "#BBBBBB", +} +plt.switch_backend("TkAgg") +plt.style.use(["science", "std-colors"]) +# mat.rcParams.update({'font.size': 28}) +# mat.rcParams.update({"font.size": 16}) +mat.rcParams["font.size"] = 16 +mat.rcParams["mathtext.fontset"] = "cm" +mat.rcParams["font.family"] = "Times New Roman" +# size = 36 +# sizein = 12 + +colors = [ + cdict["blue"], + cdict["red"], + cdict["orange"], + cdict["magenta"], + cdict["cyan"], + "black", + cdict["teal"], + "grey", +] +pts = ['s', '^', 'v', 'p', 's', 'o', 'd'] + + +def errorbar_mvsrs(rs, meff_data, merr, idx, label, ax=plt.gca(), zorder=None): + if zorder is not None: + handle = ax.errorbar(rs, meff_data, merr, fmt=pts[idx], capthick=1, capsize=4, + ms=5, color=colors[idx], label=label, zorder=zorder) + else: + handle = ax.errorbar(rs, meff_data, merr, fmt=pts[idx], capthick=1, capsize=4, + ms=5, color=colors[idx], label=label) + return handle + + +def plot_mvsrs(rs, meff_data, idx, label, ls='-', ax=plt.gca(), rs_HDL=None, meff_HDL=None, zorder=None): + # Add data in the high-density limit to the fit, if provided + if (rs_HDL is not None) and (meff_HDL is not None): + rslist = pd.unique(np.concatenate([rs, rs_HDL])) + mdatalist = pd.unique(np.concatenate([meff_data, meff_HDL])) + P = np.argsort(rslist) + rs = rslist[P] + meff_data = mdatalist[P] + print(rs) + print(meff_data) + + # mfitfunc = interpolate.PchipInterpolator(rs, meff_data) + mfitfunc = interpolate.Akima1DInterpolator(rs, meff_data) + # xgrid = np.arange(0, 6.2, 0.02) + xgrid = np.arange(0, 1.2, 0.002) + # ax.plot(rs, meff_data, 'o', ms=10, color=colors[idx]) + # ax.plot(xgrid, mfitfunc(xgrid), ls=ls, lw=2, color=colors[idx], label=label) + if zorder is not None: + handle, = ax.plot(xgrid, mfitfunc(xgrid), ls=ls, + color=colors[idx], label=label, zorder=zorder) + else: + handle, = ax.plot(xgrid, mfitfunc(xgrid), ls=ls, + color=colors[idx], label=label) + + yfit = np.ma.masked_invalid(mfitfunc(xgrid)) + # print(yfit) + print("Turning point: rs = ", xgrid[np.argmin(yfit)]) + print("Effective mass ratio at turning point: ", np.min(yfit)) + return handle + + +# Taylor series for m* / m in the high-density limit to leading order in rs in 2D +# according to Giuliani & Vignale, Quantum Theory of the Electron Liquid (2008). +# This formula is incorrect; see below. +def high_density_limit_giuliani_vignale(rs): + # c_2d = 1 / np.pi + # alpha_2d = 1 / np.sqrt(2.0) # original formula from G&V + # # return 1 + c_2d * alpha_2d * rs * np.log(rs) / np.pi + # return 1 + rs * np.log(rs) / (np.sqrt(2) * np.pi * np.pi) + raise NotImplementedError("Incorrect formula for 2D high-density limit") + + +# Taylor series for m* / m in the high-density limit to leading order in rs in 2D +# (c.f. R. Asgari et al., PRB 79, 235324 (2009), doi:10.1103/PhysRevB.79.235324) +def high_density_limit_asgadi(rs): + return 1 + rs * np.log(rs) / (np.sqrt(2) * np.pi) + + +# # This fits our data quite well; is there an error in [G&V] / Asgadi? +# # NOTE: No, seems that Asgadi's formula is correct, and G&V's is wrong. +# def high_density_limit_emp(rs): +# c_2d = 1 / np.pi +# alpha_2d = np.sqrt(2.0) +# # alpha_2d = 1 / np.sqrt(2.0) # original formula from G&V +# return 1 + c_2d * alpha_2d * rs * np.log(rs) / np.pi +def main(): + fig, ax = plt.subplots(figsize=(5, 5)) + + m_VDMC = [1.0, 0.9675, 0.951, 0.952, 0.970] + m_VDMC_err = [0, 0.0010, 0.001, 0.002, 0.004] + rs_VDMC = [0, 0.1, 0.3, 0.5, 1] + + rs_DMC = [0, 1, 2, 3, 4, 5] + m_DMC = [1.0, 0.918, 0.879, 0.856, 0.842, 0.791] + m_DMC_err = [0, 0.006, 0.014, 0.014, 0.017, 0.01] + + # f_sigma_G0W0 = np.load("finalized_meff_results/meff_2d_sigma_G0W0_large_rs.npz") + f_sigma_G0W0 = np.load("finalized_meff_results/meff_2d_sigma_G0W0.npz") + rs_G0W0 = f_sigma_G0W0["rslist"] + m_G0W0 = f_sigma_G0W0["mefflist"] + + # High-density limit + rs_HDL_plot = np.linspace(1e-5, 0.387755102040817, num=101) + meff_HDL_plot = np.array([high_density_limit_asgadi(rs) for rs in rs_HDL_plot]) + # meff_HDL_plot = np.array([high_density_limit_giuliani_vignale(rs) for rs in rs_HDL_plot]) + + # # Use exact expression in the high-density limit for RPA(+FL) and RPT fits + # cutoff_HDL = 0.1 + # rs_HDL = rs_HDL_plot[rs_HDL_plot <= cutoff_HDL] + # meff_HDL = meff_HDL_plot[rs_HDL_plot <= cutoff_HDL] + # print(rs_HDL) + # print(meff_HDL) + + # Use RPA expression to fit the high-density limit + # (the leading-order HDL expansion converges too slowly in 2D) + cutoff_HDL = 0.05 + rs_HDL = rs_G0W0[rs_G0W0 <= cutoff_HDL] + meff_HDL = m_G0W0[rs_G0W0 <= cutoff_HDL] + print(rs_HDL) + print(meff_HDL) + + # RPA + handle1 = plot_mvsrs(rs_G0W0, m_G0W0, 2, r"RPA", '--', ax=ax) + # handle1 = plot_mvsrs(rs_G0W0, m_G0W0, 2, r"RPA", '--', ax=ax, zorder=10000) + + # High-density limit + # handle2 = plot_mvsrs(rs_HDL_plot, meff_HDL_plot, 4, + # "High-density limit [17]", "--", zorder=1000, ax=ax) + # "High-density limit [5]", "--", zorder=1000, ax=ax) + + # # High-density limit reported in Xie et al...this seems very wrong? + # x_near0, y_near0 = np.array([ + # [0., 1.], + # [0.11224489795918391, 0.9117854622441779], + # [0.18367346938775508, 0.8599153140437545], + # [0.26530612244897966, 0.8295695130557517], + # [0.387755102040817, 0.7985179957657023]]).T + # ax.plot(x_near0, y_near0, "o--", color=colors[7], + # label="High-density limit [14]", zorder=1001) + + # Xie data + rs_xie = [0.25, 0.5, 1.0, 3.0, 5.0, 10.0] + # N = 29 + m_xie_N29 = [0.9493450590994533, 0.882463202728022, 0.8075088885361558, + 0.6624456568146859, 0.5370396071086241, 0.3815095840237416] + m_xie_N29_err = [0.012286238330642787, 0.014801924633879382, 0.012908898901033937, + 0.00404809293349585, 0.0052229360479842165, 0.007245691592627612] + # N = 49 + m_xie_N49 = [0.9697659283566704, 0.9209192115756524, 0.8640514413966484, + 0.628293959920195, 0.5497751333980478, 0.4046921719547083] + m_xie_N49_err = [0.021674990617977383, 0.00811342432541565, 0.011749023191077004, + 0.009302572885392053, 0.0033228606617660738, 0.0022218086489334214] + # N = 57 + m_xie_N57 = [0.8972423881298187, 0.7974929235841779, 0.7482061436659886, + 0.5901231585641507, 0.4869549111001582, 0.3877645835702172] + m_xie_N57_err = [0.025544403804267292, 0.01605710503593936, 0.029722120598245434, + 0.018958500988648527, 0.017426480375743132, 0.003010231602124497] + + # Plot Xie data + handle3 = errorbar_mvsrs(rs_xie, m_xie_N29, m_xie_N29_err, + 0, r"NCT $(N_e = 29)$ [14]", ax=ax) + handle4 = errorbar_mvsrs(rs_xie, m_xie_N49, m_xie_N49_err, + 1, r"NCT $(N_e = 49)$ [14]", ax=ax) + handle5 = errorbar_mvsrs(rs_xie, m_xie_N57, m_xie_N57_err, + 6, r"NCT $(N_e = 57)$ [14]", ax=ax) + + print("\nPlotting our data") + handle6 = errorbar_mvsrs(rs_VDMC, m_VDMC, m_VDMC_err, + 5, "This work", zorder=30, ax=ax) + # plot_mvsrs(rs_VDMC, m_VDMC, 5, "", '-', ax=ax) + plot_mvsrs(rs_VDMC, m_VDMC, 5, "", '-', rs_HDL=rs_HDL, meff_HDL=meff_HDL, ax=ax) + + ax.set_xlabel(r"$r_s$") + ax.set_ylabel(r"$m^*/m$") + ax.annotate(r"2D", xy=(0.875, 0.9), xycoords="axes fraction") + + # ax.set_xlim(0, 0.25) + ax.set_xlim(0, 1.05) + ax.set_ylim(0.56, 1.12) + # ax.set_ylim(0.56, 1.12) + # ax.set_yticks([0.65, 0.7, 0.75, 0.8, 0.85, 0.9, 0.95, 1.0, 1.05, 1.1]) + + # ax.set_xlim(0, 5) + # ax.set_ylim(0.4, 1.008) + + # ax.set_ylim(0.942, 1.008) + # ax.set_ylim(0.765, 1.135) + + # Assemble legends + l1_handles = [handle1] + # l1_handles = [handle1, handle2] + l2_handles = [handle3, handle4, handle5, handle6] + top_legend = plt.legend(handles=l1_handles, loc="upper left", fontsize=14) + bottom_legend = plt.legend(handles=l2_handles, loc="lower left", fontsize=14) + ax.add_artist(top_legend) + ax.add_artist(bottom_legend) + + # Save the figure + plt.savefig("meff_2DUEG.pdf") + return + + +if __name__ == "__main__": + main() diff --git a/example/sigma/plot_meff3d.py b/example/sigma/plot_meff3d.py new file mode 100644 index 0000000..186664b --- /dev/null +++ b/example/sigma/plot_meff3d.py @@ -0,0 +1,219 @@ +#!/usr/bin/python3 +import scienceplots +import numpy as np +import pandas as pd +from scipy import interpolate +import matplotlib as mat +import matplotlib.pyplot as plt +from mpl_toolkits.axes_grid1.inset_locator import inset_axes + +cdict = { + "blue" : "#0077BB", + "cyan" : "#33BBEE", + "teal" : "#009988", + "orange" : "#EE7733", + "red" : "#CC3311", + "magenta" : "#EE3377", + "grey" : "#BBBBBB", +} +# plt.switch_backend("TkAgg") +plt.style.use(["science", "std-colors"]) +# mat.rcParams.update({'font.size': 28}) +# mat.rcParams.update({"font.size": 16}) +mat.rcParams["font.size"] = 16 +mat.rcParams["mathtext.fontset"] = "cm" +mat.rcParams["font.family"] = "Times New Roman" +# size = 36 +# sizein = 12 + +points = ['o','^','s','v','p','<','h','>'] +# Colormap = ["blue", "red", "orange", "violet", "green", "black", "darkblue"] +# Color_beta = {0.125: "red", 0.25: "orange", 0.5: "violet", 1.0: "green", 2.0: "blue", 2.5:"darkblue", 16.0: "black"} +Colormap = [ + cdict["blue"], + cdict["red"], + cdict["orange"], + cdict["magenta"], + cdict["cyan"], + "black", + cdict["teal"], + "grey", +] +# pt_beta = {0.125: 'o', 0.25: '^', 0.5: 'h', 1.0: 'v', 2.0: 'd', 2.5:'p', 16.0: 's'} +pts = ['s', '^', 'v', 'p', 's', 'o', 'd'] +# fig, axes = plt.subplots(1,2, sharex='col')#, sharey=True, gridspec_kw={'wspace': 0}) +# fig, ax1 = plt.subplots(figsize=(6, 4.6)) +# fig, ax1 = plt.subplots(figsize=(6, 4)) +fig, ax1 = plt.subplots(figsize=(5, 5)) +# fig.set_size_inches(13,10) + +# m_VDMC = [1.0, 0.95861, 0.9511, 0.9516, 0.9601, 0.968, 0.9782] +# m_VDMC_err = [0, 0.00089, 0.0021, 0.0031, 0.0022, 0.0021, 0.0025] +# rs_VDMC = [0, 0.5, 1, 2, 3, 4, 5] +m_VDMC = [1.0, 0.95893, 0.9514, 0.9516, 0.9597, 0.9692, 0.9771, 0.9842] +m_VDMC_err = [0, 0.00067, 0.0016, 0.0018, 0.0016, 0.0026, 0.0028, 0.0029] +rs_VDMC = [0, 0.5, 1, 2, 3, 4, 5, 6] + +rs_VMC = [0, 1, 2, 4, 5, 10] +# m_BFVMC = [[1.00, 0.01], [0.98, 0.01], [1.00, 0.02], [1.09,0.03],[1.28, 0.03]] +m_BFVMC = [1.0, 1.00, 0.98, 1.00, 1.09, 1.28] +m_BFVMC_err = [0, 0.01, 0.01, 0.02, 0.03, 0.03] +# m_SJVMC = [[0.96,0.01], [0.94, 0.02], [0.94, 0.02], [1.02, 0.02], [1.13, 0.03]] +m_SJVMC = [1.0, 0.96, 0.94, 0.94, 1.02, 1.13] +m_SJVMC_err = [0, 0.01, 0.02, 0.02, 0.02, 0.03] + +rs_DMC = [0, 1, 2, 3, 4, 5] +m_DMC = [1.0, 0.918, 0.879, 0.856, 0.842, 0.791] +m_DMC_err = [0, 0.006, 0.014, 0.014, 0.017, 0.01] + +f_sigma_G0W0 = np.load("finalized_meff_results/3d/rpa/meff_3d_sigma_G0W0.npz") +rs_G0W0 = f_sigma_G0W0["rslist"] +m_G0W0 = f_sigma_G0W0["mefflist"] + +# f_sigma_G0Wp = np.load("finalized_meff_results/3d/simion_giuliani/meff_3d_sigma_G0Wp.npz") +f_sigma_G0Wp = np.load("finalized_meff_results/3d/const/meff_3d_sigma_G0Wp.npz") +rs_G0Wp = f_sigma_G0Wp["rslist"] +m_G0Wp = f_sigma_G0Wp["mefflist"] + +# f_sigma_G0Wpm = np.load("finalized_meff_results/3d/simion_giuliani/meff_3d_sigma_G0Wpm.npz") +f_sigma_G0Wpm = np.load("finalized_meff_results/3d/const/meff_3d_sigma_G0Wpm.npz") +rs_G0Wpm = f_sigma_G0Wpm["rslist"] +m_G0Wpm = f_sigma_G0Wpm["mefflist"] + +f_tree_level_G0W0 = np.load("finalized_meff_results/3d/rpa/meff_3d_tree_level_G0W0.npz") +rs_tree_level_G0W0 = f_tree_level_G0W0["rslist"] +m_tree_level_G0W0 = f_tree_level_G0W0["mefflist"] + +f_tree_level_G0Wp = np.load("finalized_meff_results/3d/const/meff_3d_tree_level_G0Wp.npz") +rs_tree_level_G0Wp = f_tree_level_G0Wp["rslist"] +m_tree_level_G0Wp = f_tree_level_G0Wp["mefflist"] + +# rs_RPA = [0, 1, 2, 3, 4, 5, 6] +# # m_RPA = [[0.97, 0], [0.992,0], [1.016,0] [1.039,0], [1.059, 0]] +# # m_Gp = [[0.952, 0], [0.951, 0], [0.956, 0], [0.962, 0], [0.968, 0]] +# # m_Gpm = [[0.957, 0], [0.966, 0], [0.983, 0], [1.005, 0], [1.028,0]] +# m_G0W0 = [1.0, 0.970, 0.992, 1.016, 1.039, 1.059, 1.078] +# m_Gp = [1.0, 0.952, 0.951, 0.956, 0.962, 0.968, 0.973] +# m_Gpm = [1.0, 0.957, 0.966, 0.983, 1.005, 1.028, 1.055] + +def errorbar_mvsrs(rs, meff_data, merr, idx, label, ax=ax1, zorder=None): + if zorder is not None: + handle = ax.errorbar(rs, meff_data, merr, fmt=pts[idx], capthick=1, capsize=4, + ms=5, color=Colormap[idx], label=label, zorder=zorder) + else: + handle = ax.errorbar(rs, meff_data, merr, fmt=pts[idx], capthick=1, capsize=4, + ms=5, color=Colormap[idx], label=label) + return handle + +def plot_mvsrs(rs, meff_data, idx, label, ls='-', ax=ax1, rs_HDL=None, meff_HDL=None, zorder=None): + # Add data in the high-density limit to the fit, if provided + if (rs_HDL is not None) and (meff_HDL is not None): + rslist = pd.unique(np.concatenate([rs, rs_HDL])) + mdatalist = pd.unique(np.concatenate([meff_data, meff_HDL])) + P = np.argsort(rslist) + rs = rslist[P] + meff_data = mdatalist[P] + print(rs) + print(meff_data) + + # mfitfunc = interpolate.PchipInterpolator(rs, meff_data) + mfitfunc = interpolate.Akima1DInterpolator(rs, meff_data) + # xgrid = np.arange(0, 6.2, 0.02) + xgrid = np.arange(0, 6.2, 0.02) + # ax.plot(rs, meff_data, 'o', ms=10, color=Colormap[idx]) + # ax.plot(xgrid, mfitfunc(xgrid), ls=ls, lw=2, color=Colormap[idx], label=label) + if zorder is not None: + handle, = ax.plot(xgrid, mfitfunc(xgrid), ls=ls, color=Colormap[idx], label=label, zorder=zorder) + else: + handle, = ax.plot(xgrid, mfitfunc(xgrid), ls=ls, color=Colormap[idx], label=label) + + yfit = np.ma.masked_invalid(mfitfunc(xgrid)) + # print(yfit) + print("Turning point: rs = ", xgrid[np.argmin(yfit)]) + print("Effective mass ratio at turning point: ", np.min(yfit)) + return handle + +# Taylor series for m* / m in the high-density limit to leading order in rs in 3D +# (c.f. Giuliani & Vignale, Quantum Theory of the Electron Liquid, 2008, p. 500) +def high_density_limit(rs): + alpha = (4.0 / (9.0 * np.pi))**(1.0 / 3.0) + return 1 + alpha * rs * np.log(rs) / (2.0 * np.pi) + +# High-density limit +rs_HDL_plot = np.linspace(1e-5, 0.35, num=101) +meff_HDL_plot = np.array([high_density_limit(rs) for rs in rs_HDL_plot]) + +# Use exact expression in the high-density limit for RPA(+FL) and RPT fits +cutoff_HDL = 0.1 +rs_HDL = rs_HDL_plot[rs_HDL_plot <= cutoff_HDL] +meff_HDL = meff_HDL_plot[rs_HDL_plot <= cutoff_HDL] +print(rs_HDL) +print(meff_HDL) + +# High-density limit +# plot_mvsrs(rs_HDL_plot, meff_HDL_plot, 7, "HDL", "--", zorder=1000) + +# m_QMC = [m_DMC, m_SJVMC] +# m_QMC_errs = [m_DMC_err, m_SJVMC_err] +# labels = ["DMC (2021)", "VMC (2023)"] +# idx = 0 +# for (mdat, merr, label) in zip(m_QMC, m_QMC_errs, labels): + # errorbar_mvsrs(rs_VMC, mdat, merr, idx, label) + # idx = idx + 1 +handle1 = errorbar_mvsrs(rs_DMC, m_DMC, m_DMC_err, 0, "DMC [12]", zorder=10) +handle2 = errorbar_mvsrs(rs_VMC, m_SJVMC, m_SJVMC_err, 1, "VMC [13]", zorder=20) + +idx = 2 +l1_handles = [] +rsdats = [rs_G0W0, rs_tree_level_G0W0, rs_tree_level_G0Wp] +mdats = [m_G0W0, m_tree_level_G0W0, m_tree_level_G0Wp] +labels = [r"RPA", r"Tree-level $G_0 W_0$", r"Tree-level $G_0 W_+$"] +for (rsdat, mdat, label) in zip(rsdats, mdats, labels): + print("\nPlotting ", label) + handle = plot_mvsrs(rsdat, mdat, idx, label, '--', rs_HDL=rs_HDL, meff_HDL=meff_HDL) + l1_handles.append(handle) + idx = idx + 1 + +l1_handles = [] +# m_RPA = [m_G0W0] +rs_RPA = [rs_G0W0, rs_G0Wp, rs_G0Wpm] +m_RPA = [m_G0W0, m_G0Wp, m_G0Wpm] +# merr = np.zeros(len(rs_RPA)) +labels = [r"$G_0 W_0$", r"$G_0 W_+$", r"$G_0 W_\\pm$"] +# labels = [r"RPA"] +# labels = [r"$G_0 W_0$"] +# labels = [r"$G_0 W_0$", r"$G_+$ [15]", r"$G_+$\,\&\,$G_-$ [15]"] +idx = 2 +for (mdat, label) in zip(rs_RPA, m_RPA, labels): + print("\nPlotting ", label) + handle = plot_mvsrs(rs_RPA, mdat, idx, label, '--', rs_HDL=rs_HDL, meff_HDL=meff_HDL) + l1_handles.append(handle) + idx = idx + 1 + +# Add points at rs = 0 +# rs_HDL = np.insert(rs_HDL, 0, 0.0) +# meff_HDL = np.insert(meff_HDL, 0, 1.0) + +handle3 = errorbar_mvsrs(rs_VDMC, m_VDMC, m_VDMC_err, idx, "This work", zorder=30) +# rs_VDMC.append(5.2) +# m_VDMC.append(0.98) +print("\nPlotting our data") +plot_mvsrs(rs_VDMC, m_VDMC, idx, "", '-', rs_HDL=rs_HDL, meff_HDL=meff_HDL) + +ax1.set_xlabel(r"$r_s$") +ax1.set_ylabel(r"$m^*/m$") +ax1.set_xlim(0, 6.2) +ax1.set_ylim(0.765, 1.135) +ax1.annotate(r"3D", xy=(0.875, 0.9), xycoords="axes fraction") + +# Assemble legends +l2_handles = [handle1, handle2, handle3] +top_legend = plt.legend(handles=l1_handles, loc="upper left", fontsize=14) +bottom_legend = plt.legend(handles=l2_handles, loc="lower left", fontsize=14) +ax1.add_artist(top_legend) +ax1.add_artist(bottom_legend) +ax1.set_xticks([0, 1, 2, 3, 4, 5, 6]) +ax1.set_yticks([0.8, 0.85, 0.9, 0.95, 1.0, 1.05, 1.1]) + +# Save the figure +plt.savefig("meff_3DUEG.pdf") diff --git a/example/sigma/plot_meff3d_comparisons_g0w.jl b/example/sigma/plot_meff3d_comparisons_g0w.jl new file mode 100644 index 0000000..bb2b6f4 --- /dev/null +++ b/example/sigma/plot_meff3d_comparisons_g0w.jl @@ -0,0 +1,197 @@ +using PyCall +using PyPlot +# using Printf +using ElectronGas, ElectronLiquid, Parameters +using Lehmann, GreenFunc, CompositeGrids, CurveFit + +@pyimport numpy as np # for saving/loading numpy data +@pyimport scienceplots # for style "science" +@pyimport scipy.interpolate as interp + +# Vibrant qualitative colour scheme from https://personal.sron.nl/~pault/ +const cdict = Dict([ + "orange" => "#EE7733", + "blue" => "#0077BB", + "cyan" => "#33BBEE", + "magenta" => "#EE3377", + "red" => "#CC3311", + "teal" => "#009988", + "grey" => "#BBBBBB", +]); +style = PyPlot.matplotlib."style" +style.use(["science", "std-colors"]) +const color = [ + "black", + cdict["orange"], + cdict["blue"], + cdict["cyan"], + cdict["magenta"], + cdict["red"], + cdict["teal"], +] +rcParams = PyPlot.PyDict(PyPlot.matplotlib."rcParams") +rcParams["font.size"] = 16 +rcParams["mathtext.fontset"] = "cm" +rcParams["font.family"] = "Times New Roman" + +# Plot F1 vs rs +# fig2 = figure(figsize=(5, 5)) +fig2 = figure(figsize=(6, 6)) +ax2 = fig2.add_subplot(111) + +function plot_mvsrs(rs, meff_data, color, label, ls="-", ax=ax2; rs_HDL=nothing, meff_HDL=nothing, zorder=nothing) + # Add data in the high-density limit to the fit, if provided + if !isnothing(rs_HDL) && !isnothing(meff_HDL) + _rslist = unique([rs; rs_HDL]) + mdatalist = unique([meff_data; meff_HDL]) + P = sortperm(_rslist) + rs = _rslist[P] + meff_data = mdatalist[P] + end + + # mfitfunc = interp.PchipInterpolator(rs, meff_data) + mfitfunc = interp.Akima1DInterpolator(rs, meff_data) + xgrid = np.arange(0, maximum(_rslist) + 0.2, 0.01) + # xgrid = np.arange(0, 6.2, 0.01) + # ax.scatter(rs, meff_data; color=color, marker="o") + if isnothing(zorder) + handle, = ax.plot(xgrid, mfitfunc(xgrid), ls=ls, color=color, label=label) + else + handle, = ax.plot(xgrid, mfitfunc(xgrid), ls=ls, color=color, label=label, zorder=zorder) + end + yfit = np.ma.masked_invalid(mfitfunc(xgrid)) + # print(yfit) + # print("Turning point: rs = ", xgrid[np.argmin(yfit)]) + # print("Effective mass ratio at turning point: ", np.min(yfit)) + return handle +end + +# Taylor series for m* / m in the high-density limit to leading order in rs +# (c.f. Giuliani & Vignale, Quantum Theory of the Electron Liquid, 2008, p. 500) +function high_density_limit(x) + alpha = (4 / 9π)^(1 / 3.0) + return 1 + alpha * x * log(x) / 2π +end + +# High-density limit +rs_HDL_plot = collect(LinRange(1e-5, 0.35, 101)) +meff_HDL_plot = high_density_limit.(rs_HDL_plot) + +# Use exact expression in the high-density limit for RPT and Simion & Giuliani fits +cutoff_HDL = 0.1 +rs_HDL = rs_HDL_plot[rs_HDL_plot.≤cutoff_HDL] +meff_HDL = meff_HDL_plot[rs_HDL_plot.≤cutoff_HDL] +println(rs_HDL) +println(meff_HDL) + +################ +### Load data ## +################ + +# f_sigma_G0W0 = np.load("finalized_meff_results/test/meff_3d_sigma_G0W0.npz") +f_sigma_G0W0 = np.load("finalized_meff_results/3d/rpa/meff_3d_sigma_G0W0.npz") +rs_sigma_G0W0 = f_sigma_G0W0.get("rslist") +m_sigma_G0W0 = f_sigma_G0W0.get("mefflist") + +# f_sigma_G0Wp = np.load("finalized_meff_results/3d/simion_giuliani/meff_3d_sigma_G0Wp.npz") +# f_sigma_G0Wp = np.load("finalized_meff_results/test/meff_3d_sigma_G0Wp.npz") +f_sigma_G0Wp = np.load("finalized_meff_results/3d/const/meff_3d_sigma_G0Wp.npz") +rs_sigma_G0Wp = f_sigma_G0Wp.get("rslist") +m_sigma_G0Wp = f_sigma_G0Wp.get("mefflist") + +# f_sigma_G0Wpm = np.load("finalized_meff_results/3d/simion_giuliani/meff_3d_sigma_G0Wpm.npz") +# f_sigma_G0Wpm = np.load("finalized_meff_results/test/meff_3d_sigma_G0Wpm.npz") +f_sigma_G0Wpm = np.load("finalized_meff_results/3d/const/meff_3d_sigma_G0Wpm.npz") +rs_sigma_G0Wpm = f_sigma_G0Wpm.get("rslist") +m_sigma_G0Wpm = f_sigma_G0Wpm.get("mefflist") + +f_tree_level_G0W0 = np.load("finalized_meff_results/3d/rpa/meff_3d_tree_level_G0W0.npz") +rs_tree_level_G0W0 = f_tree_level_G0W0.get("rslist") +m_tree_level_G0W0 = f_tree_level_G0W0.get("mefflist") + +f_tree_level_G0Wp = np.load("finalized_meff_results/3d/const/meff_3d_tree_level_G0Wp.npz") +rs_tree_level_G0Wp = f_tree_level_G0Wp.get("rslist") +m_tree_level_G0Wp = f_tree_level_G0Wp.get("mefflist") + +println(m_sigma_G0W0) +println(m_sigma_G0Wp) +println(m_sigma_G0Wpm) +return + +################ +################ +################ + +# Add points at rs = 0 +for rslist in [rs_HDL, rs_sigma_G0W0, rs_sigma_G0Wp, rs_sigma_G0Wpm, rs_tree_level_G0W0, rs_tree_level_G0Wp] + if rslist[1] != 0.0 + pushfirst!(rslist, 0.0) + end +end +for mefflist in [meff_HDL, m_tree_level_G0W0, m_tree_level_G0Wp, m_sigma_G0W0, m_sigma_G0Wp, m_sigma_G0Wpm, meff_HDL_plot] + if mefflist[1] != 1.0 + pushfirst!(mefflist, 1.0) + end +end + +# Plot data +colors = [ + cdict["orange"], + cdict["blue"], + cdict["magenta"], + cdict["cyan"], + cdict["red"], + cdict["teal"], + "black", +] + +# High-density limit +# plot_mvsrs(rs_HDL_plot, meff_HDL_plot, colors[1], "High-density limit", "--"; zorder=1000) + +# Tree-level RPA +plot_mvsrs(rs_tree_level_G0W0, m_tree_level_G0W0, "black", "Tree-level \$F^+_1\$, \$G_0 W_0\$", "--"; rs_HDL=rs_HDL, meff_HDL=meff_HDL) + +# Tree-level RPA+FL +plot_mvsrs(rs_tree_level_G0Wp, m_tree_level_G0Wp, "black", "Tree-level \$F^+_1\$, \$G_0 W_+\$", ":"; rs_HDL=rs_HDL, meff_HDL=meff_HDL) + +# Self-energy G_0 W_0 +plot_mvsrs(rs_sigma_G0W0, m_sigma_G0W0, colors[1], "\$G_0 W_0\$"; rs_HDL=rs_HDL, meff_HDL=meff_HDL) + +# Self-energy G_0 W_+ (Moroni) +plot_mvsrs(rs_sigma_G0Wp, m_sigma_G0Wp, colors[2], "\$G_0 W_+\$"; rs_HDL=rs_HDL, meff_HDL=meff_HDL) + +# Self-energy G_0 W_± (Simion & Giuliani) +plot_mvsrs(rs_sigma_G0Wpm, m_sigma_G0Wpm, colors[3], "\$G_0 W_\\pm\$"; rs_HDL=rs_HDL, meff_HDL=meff_HDL) +# ax2.scatter(rspmlist, m_sigma_G0Wpm; color=colors[3], marker="v", zorder=600) + +# Simion & Giuliani self-energy G_0 W_0, G_0 W_+, and G_0 W_± results +rs_RPA = [0, 1, 2, 3, 4, 5, 6] +m_G0W0 = [1.0, 0.970, 0.992, 1.016, 1.039, 1.059, 1.078] +m_Gp = [1.0, 0.952, 0.951, 0.956, 0.962, 0.968, 0.973] +m_Gpm = [1.0, 0.957, 0.966, 0.983, 1.005, 1.028, 1.055] +# plot_mvsrs(rs_RPA, m_G0W0, "black", "\$\\Sigma_{G_0 W_0}\$", ":") +# plot_mvsrs(rs_RPA, m_Gp, "black", "\$\\Sigma_{G_0 W_+}\$", "-.") +# plot_mvsrs(rs_RPA, m_G0W0, colors[5], "\$\\Sigma_{G_0 W_0}\$ (Simion, 2008)", "--"; rs_HDL=rs_HDL, meff_HDL=meff_HDL) +# plot_mvsrs(rs_RPA, m_Gp, colors[6], "\$\\Sigma_{G_0 W_+}\$ (Simion, 2008)", "--"; rs_HDL=rs_HDL, meff_HDL=meff_HDL) +# plot_mvsrs(rs_RPA, m_Gpm, "black", "\$\\Sigma_{G_0 W_\\pm}\$", "--"; rs_HDL=rs_HDL, meff_HDL=meff_HDL) +ax2.scatter(rs_RPA, m_G0W0; color=colors[4], marker="^", label="\$G_0 W_0\$ (Ref. [16])", zorder=700) +ax2.scatter(rs_RPA, m_Gp; color=colors[5], marker="s", label="\$G_0 W_+\$ (Ref. [16])", zorder=800) +ax2.scatter(rs_RPA, m_Gpm; color=colors[6], marker="D", label="\$G_0 W_\\pm\$ (Ref. [16])", zorder=900) + +# RPT Monte Carlo results for full m* / m +m_VDMC = [1.0, 0.95893, 0.9514, 0.9516, 0.9597, 0.9692, 0.9771, 0.9842] +m_VDMC_err = [0, 0.00067, 0.0016, 0.0018, 0.0016, 0.0026, 0.0028, 0.0029] +rs_VDMC = [0, 0.5, 1, 2, 3, 4, 5, 6] +ax2.errorbar(rs_VDMC, m_VDMC, m_VDMC_err; fmt="o", capthick=1, capsize=4, ms=5, color="black", label="RPT (This work)", zorder=1000) +plot_mvsrs(rs_VDMC, m_VDMC, "black", nothing; rs_HDL=rs_HDL, meff_HDL=meff_HDL) + +legend(loc="best", fontsize=12) +# legend(loc="best", ncol=2, columnspacing=0.45, fontsize=10) +# legend(loc="best", ncol=2, columnspacing=0.45) +# legend(loc=(0.09, 0.625)) +# legend(loc=(0.1, 0.5)) +ylabel("\$m^*/m\$") +xlabel("\$r_s\$") +# ylim(0.94, 1.02) +tight_layout() +savefig("meff_3DUEG_comparisons.pdf") diff --git a/example/sigma/plot_meff3d_convergence.jl b/example/sigma/plot_meff3d_convergence.jl new file mode 100644 index 0000000..a070520 --- /dev/null +++ b/example/sigma/plot_meff3d_convergence.jl @@ -0,0 +1,511 @@ +using UniElectronGas +using PyCall +using PyPlot +using DelimitedFiles +using CurveFit +using Measurements + +@pyimport scienceplots # `import scienceplots` is required as of version 2.0.0 +@pyimport scipy.interpolate as interp +@pyimport matplotlib.gridspec as gridspec + +include("../input.jl") + +cdict = Dict([ + "blue" => "#0077BB", + "cyan" => "#33BBEE", + "teal" => "#009988", + "orange" => "#EE7733", + "red" => "#CC3311", + "magenta" => "#EE3377", + "grey" => "#BBBBBB", +]) +style = PyPlot.matplotlib."style" +style.use(["science", "std-colors"]) +const color = [ + "black", + cdict["orange"], + cdict["blue"], + cdict["cyan"], + cdict["magenta"], + cdict["red"], + cdict["teal"], +] +rcParams = PyPlot.PyDict(PyPlot.matplotlib."rcParams") +rcParams["font.size"] = 16 +rcParams["mathtext.fontset"] = "cm" +rcParams["font.family"] = "Times New Roman" + +modestr = "" +if spin != 2 + modestr *= "_spin$(spin)" +end +if ispolarized + modestr *= "_polarized" +end +if isLayered2D + modestr *= "_layered" +end + +# rₛ ↦ λ*(rₛ), d = 3 +const fixed_lambda_optima_3d = Dict( + 0.5 => 3.5, + 1.0 => 1.75, + 2.0 => 2.0, + # 2.0 => 2.25, + 3.0 => 1.5, + 4.0 => 1.25, + # 4.0 => 1.125, + 5.0 => 1.125, + 6.0 => 1.0, +) + +# Two lambda points to plot for convergence tests +# Where possible, we take: (1) the chosen optimum λ*(rₛ) and (2) the largest calculated λ +# NOTE: At rs = 5, λ* itself is the largest calculated λ, so we compare with smaller λ = 0.875 +const lambdas_meff_convergence_plot_3d = Dict( + 0.5 => [3.5, 5.0], + 1.0 => [1.75, 2.0], + 2.0 => [2.0, 2.25], + 3.0 => [1.5, 2.0], + 4.0 => [1.25, 1.5], + # 4.0 => [1.125, 1.5], + 5.0 => [1.125, 0.875], + 6.0 => [1.0, 0.75], +) + +function spline(x, y, e; xmin=0.0, xmax=x[end]) + # generate knots with spline without constraints + w = 1.0 ./ e + spl = interp.UnivariateSpline(x, y; w=w, k=3) + __x = collect(LinRange(xmin, xmax, 1000)) + yfit = spl(__x) + return __x, yfit +end + +function spline_with_bc(x, y, e; xmin=0.0, xmax=x[end]) + _x, _y = deepcopy(x), deepcopy(y) + _w = 1.0 ./ e + + #enforce left boundary condition: zero derivative at 1/N → 0 + rescale = 10000 + pushfirst!(_x, 0.0) + pushfirst!(_y, y[1] / _w[1]) + pushfirst!(_w, _w[1] * rescale) + + # generate knots with spline without constraints + spl = interp.UnivariateSpline(_x, _y; w=_w, k=3) + __x = collect(LinRange(xmin, xmax, 1000)) + yfit = spl(__x) + return __x, yfit +end + +# NOTE: assumes the following row format: +# | rs | beta | mass2 | order | mean_1 ± error_1 | ... | mean_N ± error_N | +function load_from_dlm(filename, mass2; rs=rs[1], beta=beta[1], verbose=false) + data = readdlm(filename) + num_data = size(data)[1] + idx = 0 + currMaxOrder = 0 + for i in 1:num_data + if data[i, 1] == rs && data[i, 3] == mass2 + idx = i + if data[i, 4] > currMaxOrder > 0 + println("(lambda = $(mass2)) Promoting from order $(currMaxOrder) to $(data[i, 4])") + currMaxOrder = data[i, 4] + end + end + end + @assert idx != 0 "Data for rs = $(rs), mass2 = $(mass2) not found in file $(filename)" + _order = data[idx, 4] + mean, error = [], [], [] + for o in 1:_order + push!(mean, data[idx, 3o+2]) + push!(error, data[idx, 3o+4]) + end + # # Add padding values if this mass2 run has N < maxOrder + npad = max(0, order[1] - _order) + append!(mean, repeat([missing], npad)) + append!(error, repeat([missing], npad)) + + mean_total = mean + error_total = error + mass2_total = data[idx, 3] + if verbose + println(mean_total) + println(error_total) + println(mass2_total) + end + return mean_total, error_total, mass2_total +end +function load_from_dlm(filename; rs=rs[1], beta=beta[1], sortby="order", verbose=false) + @assert sortby in ["order", "mass2"] + + data = readdlm(filename) + num_data = size(data)[1] + mean_total, error_total, mass2_total = [], [], [] + for _mass2 in mass2 + idx = 0 + currMaxOrder = 0 + for i in 1:num_data + if data[i, 1] == rs && data[i, 3] == _mass2 + idx = i + if data[i, 4] > currMaxOrder > 0 + println("(lambda = $(_mass2)) Promoting from order $(currMaxOrder) to $(data[i, 4])") + currMaxOrder = data[i, 4] + end + end + end + idx == 0 && continue + _order = data[idx, 4] + mean, error = [], [], [] + for o in 1:_order + push!(mean, data[idx, 3o+2]) + push!(error, data[idx, 3o+4]) + end + # # Add padding values if this mass2 run has N < maxOrder + npad = max(0, order[1] - _order) + append!(mean, repeat([missing], npad)) + append!(error, repeat([missing], npad)) + # Add results for this mass2 to lists + push!(mean_total, mean) + push!(error_total, error) + push!(mass2_total, data[idx, 3]) + end + if verbose + println(mean_total) + println(error_total) + println(mass2_total) + end + + if sortby == "order" + mt = hcat(mean_total...) + et = hcat(error_total...) + mean_order, error_order = [], [] + for o in 1:order[1] + push!(mean_order, mt[o, :]) + push!(error_order, et[o, :]) + end + return mean_order, error_order, mass2_total + else # sortby == "mass2" + return mean_total, error_total, mass2_total + end +end + +function plot_all_order_convergence(; beta=beta[1]) + plot_rs = [1.0, 5.0] + num_rs = length(plot_rs) + @assert num_rs == 2 "plot_rs must be a 2-element array" + plot_lambda = [fixed_lambda_optima_3d[rs] for rs in plot_rs] + + # figure(figsize=(4, 4 * num_rs)) + figure(figsize=(4, 4 * num_rs)) + label_locs = [(4.4, 1.1125), (1.4, 0.935), (1.975, 1.02)] + # label_locs = [(2.2, 1.0825), (1.5, 0.9425), (1.85, 1.0275)] + labels = [ + # "\$1 + \\partial_{\\xi_k} \\text{Re}\\Sigma(k, 0) \\big|_{k = k_F}\$", + "\$D\$", + "\$Z\$", + "\$m / m^* = Z \\cdot D\$", + ] + # label_locs = [(1.0, 0.875), (3.8, 1.055), (2.6, 0.925)] + # labels = [ + # "\$(1 + \\delta m)^{-1}\$", + # "\$(1 - \\delta s)\$", + # "\$m^* / m\$", + # # "\$(1 + \\delta m)\$", + # ] + + # Helper function to plot a single subplot + function plot_at_rs(i, rs, lambda; ax0=nothing) + if isnothing(ax0) + ax = plt.subplot(num_rs, 1, i) + else + ax = plt.subplot(num_rs, 1, i, sharex=ax0) + end + filenames = [ + dispersion_ratio_filename, + zfactor_filename, + inverse_meff_filename, + # inverse_dispersion_ratio_filename, + # zinv_filename, + # meff_filename, + ] + colors = [ + cdict["red"], + cdict["blue"], + "black", + ] + for (j, (filename, color)) in enumerate(zip(filenames, colors)) + means, errors, lambda = load_from_dlm(filename, lambda; rs=rs) + valid_means = collect(skipmissing(means)) + valid_errors = collect(skipmissing(errors)) + x = collect(eachindex(valid_means)) + yval = valid_means + yerr = valid_errors + ax.errorbar( + x, + yval, + yerr=yerr, + color=color, + capsize=4, + fmt="o--", + zorder=10 * j, + ) + if i == 1 + println(labels[j], " ", label_locs[j]) + ax.annotate(labels[j], xy=label_locs[j], xycoords="data") + end + if j == 3 + # Rough estimate of total error using the last 3 orders + d1 = abs(yval[end] - yval[end-1]) + d2 = abs(yval[end] - yval[end-2]) + error_estimate = yerr[end] + max(d1, d2) + meff_estimate = measurement(yval[end], error_estimate) + ax.axhspan( + yval[end] - error_estimate, + yval[end] + error_estimate; + color=cdict["grey"], + ) + ax.axhline(yval[end]; linestyle="--", color="dimgrey") + println("rs = $rs, λ = $lambda:\tm/m* ≈ $meff_estimate") + end + end + # ax.set_ylim(0.85, 1.1) + ax.set_xticks(collect(1:order[1])) + ax.legend(; title="\$r_s = $(Int(rs))\$", loc="upper left") + return ax + end + + # first subplot + ax0 = plot_at_rs(1, plot_rs[1], plot_lambda[1]) + # ax0.set_ylim(0.85, 1.1) + plt.setp(ax0.get_xticklabels(), visible=false) # use shared x-axis + + # second subplot + ax1 = plot_at_rs(2, plot_rs[2], plot_lambda[2]; ax0=ax0) + ax1.set_xlabel("Perturbation order \$N\$") + + # remove last tick label for the second subplot + yticks = ax1.yaxis.get_major_ticks() + yticks[end].label1.set_visible(false) + + # remove vertical gap between subplots + plt.subplots_adjust(hspace=0.0) + + plt.savefig("meff$(dim)d_cancellations_vs_N.pdf") + # plt.savefig("meff$(dim)d_rs$(plot_rs)_beta$(beta)$(modestr)_with_cancellations_vs_N.pdf") +end + +function plot_meff_order_convergence(; + beta=beta[1], + plot_rs=range(1.0, 5.0), + plot_lambdas=[lambdas_meff_convergence_plot_3d[rs] for rs in plot_rs], +) + num_rs = length(plot_rs) + figure(figsize=(4 * num_rs, 4)) + for (i, (rs, lambdas)) in enumerate(zip(plot_rs, plot_lambdas)) + subplot(1, num_rs, i) + for (j, lambda) in enumerate(lambdas) + means, errors, lambda = load_from_dlm(meff_filename, lambda; rs=rs) + valid_means = collect(skipmissing(means)) + valid_errors = collect(skipmissing(errors)) + x = collect(eachindex(valid_means)) + yval = valid_means + yerr = valid_errors + starstr = j == 1 ? "^*" : "" + errorbar( + x, + yval, + yerr=yerr, + color=color[j+1], + capsize=4, + fmt="o--", + label="\$\\lambda$starstr = $lambda\$", + zorder=10 * j, + ) + # Rough estimate of total error using the last 3 orders + d1 = abs(yval[end] - yval[end-1]) + d2 = abs(yval[end] - yval[end-2]) + error_estimate = yerr[end] + max(d1, d2) + meff_estimate = measurement(yval[end], error_estimate) + axhspan( + yval[end] - error_estimate, + yval[end] + error_estimate; + color=color[j+1], + alpha=0.2, + ) + axhline(yval[end]; linestyle="-", color=color[j+1], alpha=0.6) + if lambda == fixed_lambda_optima_3d[rs] + println("rs = $rs, λ = $lambda:\tm*/m ≈ $meff_estimate") + end + end + xticks(collect(1:order[1])) + xlabel("Perturbation order \$N\$") + if i == 1 + ylabel("\$m^* / m\$") + end + legend(; title="\$r_s = $(rs)\$", loc="best") + end + tight_layout() + savefig("meff$(dim)d_rs$(plot_rs)_beta$(beta)$(modestr)_vs_N.pdf") +end + +function plot_meff_lambda_convergence(maxOrder=order[1]; rs=rs[1], beta=beta[1]) + meff_means, meff_errors, _mass2 = load_from_dlm(meff_filename; sortby="order") + + figure(figsize=(6, 4)) + xmin_plot = Inf + xmax_plot = -Inf + xgrid = LinRange(0.0, 5.0, 100) + for o in 1:maxOrder + valid_meff = skipmissing(meff_means[o]) + valid_errors = skipmissing(meff_errors[o]) + + idx_valid_mass2 = collect(eachindex(valid_meff)) + x = mass2[idx_valid_mass2] + yval = collect(valid_meff) + yerr = collect(valid_errors) + errorbar( + x, + yval, + yerr=yerr, + color=color[o], + capsize=4, + fmt="o", + markerfacecolor="none", + label="\$N = $o\$", + zorder=10 * o, + ) + xmin_plot = min(x[1], xmin_plot) + xmax_plot = max(x[end], xmax_plot) + if o < 5 + xfit, yfit = spline(x, yval, yerr) + plot(xfit, yfit; color=color[o], linestyle="--") + end + if o == maxOrder + println("\n(N = $o)\nλ = $x\nm*/m = $(measurement.(yval, yerr))\n") + end + end + ncol = 1 + if dim == 3 + if rs < 1 + xpad = 0.2 + elseif rs < 3 + xpad = 0.1 + elseif rs < 6 + xpad = 0.05 + else + xpad = 0.2 + end + xlim(xmin_plot - xpad, xmax_plot + xpad) + ylim(0.855, 1.0) + # Plot fixed lambda optima for rs = 1, 2 at d = 3 + if dim == 3 && rs in keys(fixed_lambda_optima_3d) + if ispolarized + lambda_optimum = fixed_lambda_optima_3d_GV_spin_polarized[rs] + else + lambda_optimum = fixed_lambda_optima_3d[rs] + end + axvline(lambda_optimum; linestyle="-", color="dimgray", zorder=-10) + end + if rs == 0.5 + columnspacing = 0.45 + ncol = 1 + xloc = 4.0 + yloc = 0.9825 + ylim(0.865, 1.005) + elseif rs == 1.0 + columnspacing = 0.9 + ncol = 1 + if ispolarized + xloc = 2.125 + yloc = 0.98 + ylim(0.83, 1.005) + if spinPolarPara == 1.0 + text( + 0.8, + 0.855, + "\$n_\\downarrow = 0\$"; + fontsize=16 + ) + else + text( + 0.68, + 0.98, + "\$\\frac{n_\\uparrow - n_\\downarrow}{n_\\uparrow + n_\\downarrow} = $spinPolarPara\$"; + fontsize=16 + ) + end + else + xloc = 2.125 + yloc = 0.98 + ylim(0.84, 1.005) + text( + 1.0, + 0.855, + "\$n_\\uparrow = n_\\downarrow\$"; + fontsize=16 + ) + end + elseif rs == 2.0 + columnspacing = 0.9 + ncol = 1 + xloc = 0.75 + yloc = 0.9825 + ylim(0.865, 1.005) + elseif rs == 3.0 + columnspacing = 0.9 + ncol = 1 + xloc = 0.6 + yloc = 0.8825 + ylim(0.865, 1.005) + elseif rs == 4.0 + columnspacing = 0.9 + ncol = 1 + xloc = 0.45 + yloc = 0.905 + ylim(0.89, 1.005) + elseif rs == 5.0 + columnspacing = 1.8 + ncol = 1 + xloc = 0.55 + yloc = 1.0025 + ylim(0.915, 1.02) + elseif rs == 6.0 + columnspacing = 0.9 + ncol = 2 + xloc = 1.125 + yloc = 1.0 + xlim(0.3, 2.1) + ylim(0.965, 1.005) + end + xmin, xmax = xlim() + ymin, ymax = ylim() + if rs < 1 + xstep = 1.0 + elseif rs < 4 + xstep = 0.5 + else + xstep = 0.25 + end + big_xticks = collect(range(0.0, 7.0, step=xstep)) + big_yticks = collect(range(0.8, 1.2, step=0.025)) + end + text( + xloc, + yloc, + "\$r_s = $(rs),\\, \\beta \\hspace{0.1em} \\epsilon_F = $(beta)\$"; + fontsize=16 + ) + legend(; loc="lower right", ncol=ncol, columnspacing=columnspacing) + xlabel("\$\\lambda\$ (Ry)") + ylabel("\$m^* / m\$") + savefig("meff$(dim)d_rs$(rs)_beta$(beta)$(modestr)_vs_lambda.pdf") +end + +if abspath(PROGRAM_FILE) == @__FILE__ + plot_all_order_convergence() + # plot_meff_lambda_convergence() + # plot_meff_order_convergence(plot_rs=[0.5, 1.0, 2.0, 3.0, 4.0, 5.0, 6.0]) +end \ No newline at end of file diff --git a/example/sigma/plot_meff3d_tree_level.jl b/example/sigma/plot_meff3d_tree_level.jl new file mode 100644 index 0000000..5738b3b --- /dev/null +++ b/example/sigma/plot_meff3d_tree_level.jl @@ -0,0 +1,363 @@ +using PyCall +using PyPlot +# using Printf +using ElectronGas, ElectronLiquid, Parameters +using Lehmann, GreenFunc, CompositeGrids, CurveFit + +@pyimport numpy as np # for saving/loading numpy data +@pyimport scienceplots # for style "science" +@pyimport scipy.interpolate as interp + +# Vibrant qualitative colour scheme from https://personal.sron.nl/~pault/ +const cdict = Dict([ + "orange" => "#EE7733", + "blue" => "#0077BB", + "cyan" => "#33BBEE", + "magenta" => "#EE3377", + "red" => "#CC3311", + "teal" => "#009988", + "grey" => "#BBBBBB", +]); +style = PyPlot.matplotlib."style" +style.use(["science", "std-colors"]) +const color = [ + "black", + cdict["orange"], + cdict["blue"], + cdict["cyan"], + cdict["magenta"], + cdict["red"], + cdict["teal"], +] +rcParams = PyPlot.PyDict(PyPlot.matplotlib."rcParams") +rcParams["font.size"] = 16 +rcParams["mathtext.fontset"] = "cm" +rcParams["font.family"] = "Times New Roman" + +function spline(x, y, e; xmin=0.0, xmax=x[end]) + # generate knots with spline without constraints + w = 1.0 ./ e + spl = interp.UnivariateSpline(x, y; w=w, k=3) + __x = collect(LinRange(xmin, xmax, 1000)) + yfit = spl(__x) + return __x, yfit +end + +function get_Fs(rs) + return get_Fs_PW(rs) + # if rs < 1.0 || rs > 5.0 + # return get_Fs_DMC(rs) + # else + # return get_Fs_PW(rs) + # end +end + +""" +Get the symmetric l=0 Fermi-liquid parameter F⁰ₛ from DMC data of +Moroni, Ceperley & Senatore (1995) [Phys. Rev. Lett. 75, 689]. +""" +function get_Fs_DMC(rs) + return error("Not yet implemented!") +end + +""" +Get the symmetric l=0 Fermi-liquid parameter F⁰ₛ via interpolation of the +compressibility ratio data of Perdew & Wang (1992) [Phys. Rev. B 45, 13244]. +""" +@inline function get_Fs_PW(rs) + # if rs < 1.0 || rs > 5.0 + # @warn "The Perdew-Wang interpolation for Fs may " * + # "be inaccurate outside the metallic regime!" + # end + kappa0_over_kappa = 1.0025 - 0.1721rs - 0.0036rs^2 + # F⁰ₛ = κ₀/κ - 1 + return kappa0_over_kappa - 1.0 +end + +function main() + # System parameters + dim = 3 + mass2 = 1e-8 + # beta = 40.0 + beta = 1000.0 + + # rslist = [1.0, 5.0] + # rslist = [0.5, 1.0, 2.0, 3.0, 4.0, 5.0, 6.0] + rslist = collect(LinRange(0.01, 6.0, 201)) + make_rs_plot = rslist != [1.0, 5.0] + make_angular_plot = rslist == [1.0, 5.0] + + # rs_Fsm1 = 5.24881 # Fs(rs ≈ 5.24881) = -1 + # rslist = [rs_Fsm1] + # make_rs_plot = false + # make_angular_plot = false + + int_type = :ko_const + # int_type = :ko_takada + # int_type = :ko_moroni + + if int_type == :ko_const + kotypestring = "const. \$f_+\$" + elseif int_type == :ko_takada + kotypestring = "Takada \$f_+\$" + elseif int_type == :ko_moroni + kotypestring = "Moroni \$f_+\$" + end + + color = [ + [cdict["orange"], cdict["magenta"], cdict["red"]], + [cdict["blue"], cdict["cyan"], cdict["teal"]], + ] + + # Plot angular dependence and average of RPA(+FL) integrands + if make_angular_plot + fig = figure(figsize=(6, 4)) + ax = fig.add_subplot(111) + rs1_handles = [] + rs5_handles = [] + end + if make_rs_plot + F1_rpa_vs_rs = [] + F1_rpa_fl_vs_rs = [] + F1_rpa_vs_rs = [] + F1_rpa_fl_vs_rs = [] + end + for (i, rs) in enumerate(rslist) + param = Parameter.rydbergUnit(1.0 / beta, rs) + kF, β = param.kF, param.β + + # Small params + Euv, rtol = 1000 * param.EF, 1e-11 + + nu_grid = CompositeGrid.LogDensedGrid( + :gauss, + [-1.0, 1.0], + [-1.0, 0.0, 1.0], + 20, + 1e-6, + 12, + ) + nus = nu_grid.grid + thetas = acos.(nus) + + # |k - k'| = kF sqrt(2(1 - ν)) + k_m_kps = @. kF * sqrt(2 * (1 - nus)) + + # Get Landau parameter F⁰ₛ from Perdew & Wang compressibility fit + Fs = get_Fs(rs) + if int_type == :ko_const + println("rs = $rs, Fs = $Fs, fs = $(Fs / param.NF)") + end + + # Either use constant Fs from P&W, q-dependent Takada ansatz, or Corradini fit to Moroni DMC data + if int_type == :ko_const + landaufunc = Interaction.landauParameterConst + elseif int_type == :ko_takada + landaufunc = Interaction.landauParameterTakada + elseif int_type == :ko_moroni + landaufunc = Interaction.landauParameterMoroni + end + + # Get W0_{+}(p, iωₙ=0) * Vinv (spin-symmetric static exchange part of RPA interaction divided by V) + W0_dyn, W0_inst = Interaction.RPAwrapped( + Euv, + rtol, + k_m_kps, + param; + regular=false, + ) + # W0_inst = 1 / V, W0_dyn = Wtilde, so W = (1 / W0_inst + W0_dyn) = V + Wtilde + W0_plus_static = @. (1 / W0_inst[1, 1, :] + W0_dyn[1, 1, :]) + + # Get R_{+}(p, iωₙ=0) * Vinv (spin-symmetric static exchange part of KO interaction divided by V) + R_dyn, R_inst = Interaction.KOwrapped( + Euv, + rtol, + k_m_kps, + param; + regular=false, + # int_type=:ko, + int_type=int_type, + landaufunc=landaufunc, + Fs=int_type == :ko_const ? Fs : nothing, # NOTE: NEFT uses opposite sign convention for F! + ) + # R_inst = 1 / V, R_dyn = Rtilde, so R = (1 / R_inst + R_dyn) = V + Rtilde + R_plus_static = @. (1 / R_inst[1, 1, :] + R_dyn[1, 1, :]) + + @assert maximum(imag(R_plus_static)) ≤ 1e-10 + @assert maximum(imag(W0_plus_static)) ≤ 1e-10 + + # The RPA and RPA+FL integrands are ν W0_{+}(p, iωₙ=0) and ν R_{+}(p, iωₙ=0), respectively + F1p_rpa_integrand = @. -param.NF * nus * real(W0_plus_static) + F1p_rpa_fl_integrand = @. -param.NF * nus * real(R_plus_static) + + # Perform angular integrations ν ∈ [-1, 1] + F1p_rpa = 0.5 * CompositeGrids.Interp.integrate1D(F1p_rpa_integrand / 2.0, nu_grid) + F1p_rpa_fl = 0.5 * CompositeGrids.Interp.integrate1D(F1p_rpa_fl_integrand / 2.0, nu_grid) + + # # Use ElectronLiquid.jl to compute the same quantities + # p_rpa = ParaMC(rs=rs, beta=beta, Fs=-0.0, order=1, mass2=mass2) + # p_rpa_fl = ParaMC(rs=rs, beta=beta, Fs=-Fs, order=1, mass2=mass2) + # # NOTE: NEFT uses opposite sign convention for F! + # F1p_rpa, _ = -1 .* Ver4.projected_exchange_interaction(1, p_rpa, Ver4.exchange_interaction) + # F1p_rpa_fl, _ = -1 .* Ver4.projected_exchange_interaction(1, p_rpa_fl, Ver4.exchange_interaction) + + println("\nrs = $rs:" * "\nF^{(RPA)+}_1 = $F1p_rpa" * "\nF^{(RPA+FL)+}_1 = $F1p_rpa_fl") + + + if make_angular_plot + # Plot angular dependence and average of RPA integrand + plot( + thetas, + F1p_rpa .* one.(thetas); + color=color[i][1], + linestyle="--", + ) + handle_rpa, = plot( + thetas, + F1p_rpa_integrand; + color=color[i][1], + linestyle="-", + label="RPA", + ) + # Plot angular dependence and average of RPA integrand + plot( + thetas, + F1p_rpa_fl .* one.(thetas); + color=color[i][2], + linestyle="--", + ) + handle_rpa_fl, = plot( + thetas, + F1p_rpa_fl_integrand; + color=color[i][2], + linestyle="-", + label="\$G_{+}\$", + # label="\$G_{+},\\; $kotypestring\$", + ) + handles = [handle_rpa, handle_rpa_fl] + if rs == 1 + append!(rs1_handles, handles) + elseif rs == 5 + append!(rs5_handles, handles) + end + end + if make_rs_plot + push!(F1_rpa_vs_rs, F1p_rpa) + push!(F1_rpa_fl_vs_rs, F1p_rpa_fl) + end + end + if make_angular_plot + xticks([0, π / 4, π / 2, 3π / 4, π], ["\$0\$", "\$\\pi/4\$", "\$\\pi/2\$", "\$3\\pi/4\$", "\$\\pi\$"]) + xlim(0, π) + xlabel("\$\\theta\$") + ylabel("\$P_1(\\cos\\theta) F^+_{1,1}(\\theta)\$") + + # Assemble legends + top_legend = plt.legend(handles=rs1_handles, loc=(0.5, 0.325), fontsize=14, title="\$r_s = 1\$", ncol=2, columnspacing=0.9) + bottom_legend = plt.legend(handles=rs5_handles, loc=(0.5, 0.09), fontsize=14, title="\$r_s = 5\$", ncol=2, columnspacing=0.9) + ax.add_artist(top_legend) + ax.add_artist(bottom_legend) + tight_layout() + savefig("Fp1_rpa_and_rpa_fl_angular_dependence_$(int_type).pdf") + end + if make_rs_plot + # Plot F1 vs rs + fig2 = figure(figsize=(5, 5)) + # fig2 = figure(figsize=(6, 4)) + ax2 = fig2.add_subplot(111) + + function plot_mvsrs(rs, meff_data, color, label, ls="-", ax=ax2; rs_LDL=nothing, meff_LDL=nothing, zorder=nothing) + # Add data in the low-density limit to the fit, if provided + if !isnothing(rs_LDL) && !isnothing(meff_LDL) + rslist = unique([rs; rs_LDL]) + mdatalist = unique([meff_data; meff_LDL]) + P = sortperm(rslist) + rs = rslist[P] + meff_data = mdatalist[P] + end + + # mfitfunc = interp.PchipInterpolator(rs, meff_data) + mfitfunc = interp.Akima1DInterpolator(rs, meff_data) + xgrid = np.arange(0, 6.2, 0.01) + # ax.scatter(rs, meff_data; color=color, marker="o") + if isnothing(zorder) + handle, = ax.plot(xgrid, mfitfunc(xgrid), ls=ls, color=color, label=label) + else + handle, = ax.plot(xgrid, mfitfunc(xgrid), ls=ls, color=color, label=label, zorder=zorder) + end + yfit = np.ma.masked_invalid(mfitfunc(xgrid)) + # print(yfit) + # print("Turning point: rs = ", xgrid[np.argmin(yfit)]) + # print("Effective mass ratio at turning point: ", np.min(yfit)) + return handle + end + + # Taylor series for m* / m in the low-density limit to leading order in rs + # (c.f. Giuliani & Vignale, Quantum Theory of the Electron Liquid, 2008, p. 500) + function low_density_limit(x) + alpha = (4 / 9π)^(1 / 3.0) + return 1 + alpha * x * log(x) / 2π + end + + # Low-density limit + rs_LDL_plot = collect(LinRange(1e-5, 0.35, 101)) + meff_LDL_plot = low_density_limit.(rs_LDL_plot) + + # Use exact expression in the low-density limit for RPT fit + cutoff_LDL = 0.1 + rs_LDL = rs_LDL_plot[rs_LDL_plot .≤ cutoff_LDL] + meff_LDL = meff_LDL_plot[rs_LDL_plot .≤ cutoff_LDL] + println(rs_LDL) + println(meff_LDL) + + # Add points at rs = 0 + pushfirst!(rslist, 0.0) + pushfirst!(rs_LDL, 0.0) + pushfirst!(meff_LDL, 1.0) + pushfirst!(rs_LDL_plot, 0.0) + pushfirst!(meff_LDL_plot, 1.0) + pushfirst!(F1_rpa_vs_rs, 0.0) + pushfirst!(F1_rpa_fl_vs_rs, 0.0) + + colors = [ + cdict["magenta"], + cdict["orange"], + cdict["blue"], + ] + + # Low-density limit + plot_mvsrs(rs_LDL_plot, meff_LDL_plot, colors[1], "Low-density limit", "--"; zorder=1000) + + # Tree-level RPA from ElectronLiquid.jl + plot_mvsrs(rslist, 1 .+ F1_rpa_vs_rs, colors[2], "Tree-level RPA") + # scatter(rslist, 1 .+ F1_rpa_vs_rs; color=colors[2], marker="s") + # xfit, yfit = spline(rslist, 1 .+ F1_rpa_vs_rs, 1e-6 * one.(F1_rpa_fl_vs_rs)) + # h3, = plot(xfit, yfit; color=colors[2], linestyle="-", label="RPA") + + # Tree-level RPA+FL from ElectronLiquid.jl + plot_mvsrs(rslist, 1 .+ F1_rpa_fl_vs_rs, colors[3], "Tree-level \$G_{+}\$") + # scatter(rslist, 1 .+ F1_rpa_fl_vs_rs; color=colors[3], marker="^") + # xfit2, yfit2 = spline(rslist, 1 .+ F1_rpa_fl_vs_rs, 1e-6 * one.(F1_rpa_fl_vs_rs)) + # h4, = plot(xfit2, yfit2; color=colors[3], linestyle="-", label="\$G_{+}\$") + + + # RPT Monte Carlo results for full m* / m + m_VDMC = [1.0, 0.95893, 0.9514, 0.9516, 0.9597, 0.9692, 0.9771, 0.9842] + m_VDMC_err = [0, 0.00067, 0.0016, 0.0018, 0.0016, 0.0026, 0.0028, 0.0029] + rs_VDMC = [0, 0.5, 1, 2, 3, 4, 5, 6] + ax2.errorbar(rs_VDMC, m_VDMC, m_VDMC_err; fmt="o", capthick=1, capsize=4, ms=5, color="black", label="This work", zorder=1000) + plot_mvsrs(rs_VDMC, m_VDMC, "black", nothing; rs_LDL=rs_LDL, meff_LDL=meff_LDL) + + legend(loc=(0.09, 0.625)) + # legend(loc=(0.1, 0.5)) + # legend(loc="best") + ylabel("\$m^*/m\$") + xlabel("\$r_s\$") + # ylim(0.94, 1.02) + tight_layout() + savefig("Fp1_rpa_and_rpa_fl_vs_rs_$(int_type).pdf") + end +end + +main() diff --git a/example/sigma/plot_meff3d_tree_level.py b/example/sigma/plot_meff3d_tree_level.py new file mode 100644 index 0000000..a9df6a6 --- /dev/null +++ b/example/sigma/plot_meff3d_tree_level.py @@ -0,0 +1,191 @@ +#!/usr/bin/python3 +import scienceplots +import numpy as np +import pandas as pd +from scipy import interpolate +import matplotlib as mat +import matplotlib.pyplot as plt +from mpl_toolkits.axes_grid1.inset_locator import inset_axes + +cdict = { + "blue" : "#0077BB", + "cyan" : "#33BBEE", + "teal" : "#009988", + "orange" : "#EE7733", + "red" : "#CC3311", + "magenta" : "#EE3377", + "grey" : "#BBBBBB", +} +plt.switch_backend("TkAgg") +plt.style.use(["science", "std-colors"]) +# mat.rcParams.update({'font.size': 28}) +# mat.rcParams.update({"font.size": 16}) +mat.rcParams["font.size"] = 16 +mat.rcParams["mathtext.fontset"] = "cm" +mat.rcParams["font.family"] = "Times New Roman" +# size = 36 +# sizein = 12 + +points = ['o','^','s','v','p','<','h','>'] +# Colormap = ["blue", "red", "orange", "violet", "green", "black", "darkblue"] +# Color_beta = {0.125: "red", 0.25: "orange", 0.5: "violet", 1.0: "green", 2.0: "blue", 2.5:"darkblue", 16.0: "black"} +Colormap = [ + cdict["blue"], + cdict["red"], + cdict["orange"], + cdict["magenta"], + cdict["cyan"], + "black", + cdict["teal"], + "grey", +] +# pt_beta = {0.125: 'o', 0.25: '^', 0.5: 'h', 1.0: 'v', 2.0: 'd', 2.5:'p', 16.0: 's'} +pts = ['s', '^', 'v', 'p', 's', 'o', 'd'] +# fig, axes = plt.subplots(1,2, sharex='col')#, sharey=True, gridspec_kw={'wspace': 0}) +# fig, ax1 = plt.subplots(figsize=(6, 4.6)) +# fig, ax1 = plt.subplots(figsize=(6, 4)) +fig, ax1 = plt.subplots(figsize=(5, 5)) +# fig.set_size_inches(13,10) + +# m_VDMC = [1.0, 0.95861, 0.9511, 0.9516, 0.9601, 0.968, 0.9782] +# m_VDMC_err = [0, 0.00089, 0.0021, 0.0031, 0.0022, 0.0021, 0.0025] +# rs_VDMC = [0, 0.5, 1, 2, 3, 4, 5] +m_VDMC = [1.0, 0.95893, 0.9514, 0.9516, 0.9597, 0.9692, 0.9771, 0.9842] +m_VDMC_err = [0, 0.00067, 0.0016, 0.0018, 0.0016, 0.0026, 0.0028, 0.0029] +rs_VDMC = [0, 0.5, 1, 2, 3, 4, 5, 6] + +rs_VMC = [0, 1, 2, 4, 5, 10] +# m_BFVMC = [[1.00, 0.01], [0.98, 0.01], [1.00, 0.02], [1.09,0.03],[1.28, 0.03]] +m_BFVMC = [1.0, 1.00, 0.98, 1.00, 1.09, 1.28] +m_BFVMC_err = [0, 0.01, 0.01, 0.02, 0.03, 0.03] +# m_SJVMC = [[0.96,0.01], [0.94, 0.02], [0.94, 0.02], [1.02, 0.02], [1.13, 0.03]] +m_SJVMC = [1.0, 0.96, 0.94, 0.94, 1.02, 1.13] +m_SJVMC_err = [0, 0.01, 0.02, 0.02, 0.02, 0.03] + +rs_DMC = [0, 1, 2, 3, 4, 5] +m_DMC = [1.0, 0.918, 0.879, 0.856, 0.842, 0.791] +m_DMC_err = [0, 0.006, 0.014, 0.014, 0.017, 0.01] + +rs_RPA = [0, 1, 2, 3, 4, 5, 6] +# m_RPA = [[0.97, 0], [0.992,0], [1.016,0] [1.039,0], [1.059, 0]] +# m_Gp = [[0.952, 0], [0.951, 0], [0.956, 0], [0.962, 0], [0.968, 0]] +# m_Gpm = [[0.957, 0], [0.966, 0], [0.983, 0], [1.005, 0], [1.028,0]] +m_G0W0 = [1.0, 0.970, 0.992, 1.016, 1.039, 1.059, 1.078] +m_Gp = [1.0, 0.952, 0.951, 0.956, 0.962, 0.968, 0.973] +m_Gpm = [1.0, 0.957, 0.966, 0.983, 1.005, 1.028, 1.055] + +def errorbar_mvsrs(rs, meff_data, merr, idx, label, ax=ax1, zorder=None): + if zorder is not None: + handle = ax.errorbar(rs, meff_data, merr, fmt=pts[idx], capthick=1, capsize=4, + ms=5, color=Colormap[idx], label=label, zorder=zorder) + else: + handle = ax.errorbar(rs, meff_data, merr, fmt=pts[idx], capthick=1, capsize=4, + ms=5, color=Colormap[idx], label=label) + return handle + +def plot_mvsrs(rs, meff_data, idx, label, ls='-', ax=ax1, rs_LDL=None, meff_LDL=None, zorder=None): + # Add data in the low-density limit to the fit, if provided + if (rs_LDL is not None) and (meff_LDL is not None): + rslist = pd.unique(np.concatenate([rs, rs_LDL])) + mdatalist = pd.unique(np.concatenate([meff_data, meff_LDL])) + P = np.argsort(rslist) + rs = rslist[P] + meff_data = mdatalist[P] + print(rs) + print(meff_data) + + # mfitfunc = interpolate.PchipInterpolator(rs, meff_data) + mfitfunc = interpolate.Akima1DInterpolator(rs, meff_data) + # xgrid = np.arange(0, 6.2, 0.02) + xgrid = np.arange(0, 6.2, 0.02) + # ax.plot(rs, meff_data, 'o', ms=10, color=Colormap[idx]) + # ax.plot(xgrid, mfitfunc(xgrid), ls=ls, lw=2, color=Colormap[idx], label=label) + if zorder is not None: + handle, = ax.plot(xgrid, mfitfunc(xgrid), ls=ls, color=Colormap[idx], label=label, zorder=zorder) + else: + handle, = ax.plot(xgrid, mfitfunc(xgrid), ls=ls, color=Colormap[idx], label=label) + + yfit = np.ma.masked_invalid(mfitfunc(xgrid)) + # print(yfit) + print("Turning point: rs = ", xgrid[np.argmin(yfit)]) + print("Effective mass ratio at turning point: ", np.min(yfit)) + return handle + +# Taylor series for m* / m in the low-density limit to leading order in rs +# (c.f. Giuliani & Vignale, Quantum Theory of the Electron Liquid, 2008, p. 500) +def low_density_limit(x): + alpha = (4.0 / (9.0 * np.pi))**(1.0 / 3.0) + return 1 + alpha * x * np.log(x) / (2.0 * np.pi) + +# Low-density limit +rs_LDL_plot = np.linspace(1e-5, 0.35, num=101) +meff_LDL_plot = np.array([low_density_limit(rs) for rs in rs_LDL_plot]) + +# Use exact expression in the low-density limit for RPA(+FL) and RPT fits +cutoff_LDL = 0.1 +rs_LDL = rs_LDL_plot[rs_LDL_plot <= cutoff_LDL] +meff_LDL = meff_LDL_plot[rs_LDL_plot <= cutoff_LDL] +print(rs_LDL) +print(meff_LDL) + +# Low-density limit +# plot_mvsrs(rs_LDL_plot, meff_LDL_plot, 7, "LDL", "--", zorder=1000) + +# m_QMC = [m_DMC, m_SJVMC] +# m_QMC_errs = [m_DMC_err, m_SJVMC_err] +# labels = ["DMC (2021)", "VMC (2023)"] +# idx = 0 +# for (mdat, merr, label) in zip(m_QMC, m_QMC_errs, labels): + # errorbar_mvsrs(rs_VMC, mdat, merr, idx, label) + # idx = idx + 1 +handle1 = errorbar_mvsrs(rs_DMC, m_DMC, m_DMC_err, 0, "DMC [11]", zorder=10) +handle2 = errorbar_mvsrs(rs_VMC, m_SJVMC, m_SJVMC_err, 1, "VMC [12]", zorder=20) + +l1_handles = [] +m_RPA = [m_G0W0, m_Gp, m_Gpm] +# merr = np.zeros(len(rs_RPA)) +labels = [r"$G_0W_0$", r"$G_+$", r"$G_+$\,\&\,$G_-$"] +# labels = [r"$G_0W_0$", r"$G_+$ [15]", r"$G_+$\,\&\,$G_-$ [15]"] +idx = 2 +for (mdat, label) in zip(m_RPA, labels): + print("\nPlotting ", label) + handle = plot_mvsrs(rs_RPA, mdat, idx, label, '--', rs_LDL=rs_LDL, meff_LDL=meff_LDL) + l1_handles.append(handle) + idx = idx + 1 + +# Add points at rs = 0 +# rs_LDL = np.insert(rs_LDL, 0, 0.0) +# meff_LDL = np.insert(meff_LDL, 0, 1.0) + +handle3 = errorbar_mvsrs(rs_VDMC, m_VDMC, m_VDMC_err, idx, "This work", zorder=30) +# rs_VDMC.append(5.2) +# m_VDMC.append(0.98) +print("\nPlotting our data") +plot_mvsrs(rs_VDMC, m_VDMC, idx, "", '-', rs_LDL=rs_LDL, meff_LDL=meff_LDL) + +ax1.set_xlabel(r"$r_s$") +ax1.set_ylabel(r"$m^*/m$") +ax1.set_xlim(0, 6.2) +ax1.set_ylim(0.765, 1.095) +# ax1.set_ylim(0.745, 1.095) +# ax1.set_ylim(0.78, 1.065) +# ax1.set_ylim(0.94, 0.99) +# ax1.legend(loc="upper left", fontsize=14, ncol=2) + +# Assemble legends +l2_handles = [handle1, handle2, handle3] +# top_legend = plt.legend(handles=l1_handles, loc="upper left", fontsize=14, title="Ref.[15]") +top_legend = plt.legend(handles=l1_handles, loc="upper left", fontsize=14) +bottom_legend = plt.legend(handles=l2_handles, loc="lower left", fontsize=14) +ax1.add_artist(top_legend) +ax1.add_artist(bottom_legend) +ax1.set_xticks([0, 1, 2, 3, 4, 5, 6]) +ax1.set_yticks([0.8, 0.85, 0.9, 0.95, 1.0, 1.05]) + +# ax1.set_xlabel(r"$r_s$", size=34) +# ax1.set_ylabel(r"$m^*/m$", size=34) +# ax1.tick_params(labelsize=30) +# ax1.legend(loc=2, labelspacing=1) +# ax1.legend(loc=3, fontsize=26) + +plt.savefig("meff_3DUEG.pdf") \ No newline at end of file diff --git a/example/sigma/plot_sigma_gw.jl b/example/sigma/plot_sigma_gw.jl new file mode 100644 index 0000000..5863e97 --- /dev/null +++ b/example/sigma/plot_sigma_gw.jl @@ -0,0 +1,226 @@ +using Colors +using JLD2 +using PyCall +using PyPlot +using ElectronGas, ElectronLiquid, Parameters +using Lehmann, GreenFunc, CompositeGrids, CurveFit + +@pyimport numpy as np # for saving/loading numpy data +@pyimport scienceplots # for style "science" +@pyimport scipy.interpolate as interp + +# Vibrant qualitative colour scheme from https://personal.sron.nl/~pault/ +const cdict = Dict([ + "orange" => "#EE7733", + "blue" => "#0077BB", + "cyan" => "#33BBEE", + "magenta" => "#EE3377", + "red" => "#CC3311", + "teal" => "#009988", + "grey" => "#BBBBBB", +]); +style = PyPlot.matplotlib."style" +style.use(["science", "std-colors"]) +const color = [ + "black", + cdict["orange"], + cdict["blue"], + cdict["cyan"], + cdict["magenta"], + cdict["red"], + cdict["teal"], +] +rcParams = PyPlot.PyDict(PyPlot.matplotlib."rcParams") +rcParams["font.size"] = 16 +rcParams["mathtext.fontset"] = "cm" +rcParams["font.family"] = "Times New Roman" + +function spline(x, y, e; xmin=0.0, xmax=x[end]) + # generate knots with spline without constraints + w = 1.0 ./ e + spl = interp.UnivariateSpline(x, y; w=w, k=3) + __x = collect(LinRange(xmin, xmax, 1000)) + yfit = spl(__x) + return __x, yfit +end + +function plot_mvsrs(rs, meff_data, color, label, ls="-"; rs_LDL=nothing, meff_LDL=nothing, zorder=nothing, ax=plt.gca(), lw=1.5) + # Add data in the low-density limit to the fit, if provided + if !isnothing(rs_LDL) && !isnothing(meff_LDL) + rslist = unique([rs; rs_LDL]) + mdatalist = unique([meff_data; meff_LDL]) + P = sortperm(rslist) + rs = rslist[P] + meff_data = mdatalist[P] + end + + # mfitfunc = interp.PchipInterpolator(rs, meff_data) + mfitfunc = interp.Akima1DInterpolator(rs, meff_data) + xgrid = np.arange(0, 6.2, 0.01) + # ax.scatter(rs, meff_data; color=color, marker="o") + if isnothing(zorder) + handle, = ax.plot(xgrid, mfitfunc(xgrid), ls=ls, color=color, label=label, lw=lw) + else + handle, = ax.plot(xgrid, mfitfunc(xgrid), ls=ls, color=color, label=label, zorder=zorder, lw=lw) + end + yfit = np.ma.masked_invalid(mfitfunc(xgrid)) + # print(yfit) + # print("Turning point: rs = ", xgrid[np.argmin(yfit)]) + # print("Effective mass ratio at turning point: ", np.min(yfit)) + return handle +end + +function main() + # System parameters + dim = 3 + # rs = 0.01 + # rs = 2.0 + rs = 10.0 + δK = 5e-6 + beta = 1000.0 + param = Parameter.rydbergUnit(1.0 / beta, rs, dim) + + max_steps = 100 + int_type = :rpa + if int_type == :rpa + wstring = "W_0" + elseif int_type == :ko_const_p + wstring = "W_+" + elseif int_type == :ko_const_pm + wstring = "W_{\\pm}" + end + + # Load imaginary-time self-energy data + s = [] + si = [] + local n_max + jldopen("results/sigma_GW_$(dim)d/sigma_$(int_type)_rs$(rs).jl", "r") do f + for i in 0:max_steps + try + push!(s, f["Σ_$i"]) + push!(si, f["Σ_ins_$i"]) + catch + n_max = i - 1 + break + end + end + end + + # Get static self-energies + kkfs = [] + s_iw0s = [] + si_iw0s = [] + for j in eachindex(s) + s_iw = dlr_to_imfreq(to_dlr(s[j])) + si_iw = dlr_to_imfreq(to_dlr(si[j])) + idx_iw0 = locate(s_iw.mesh[1], 0) + push!(kkfs, s[j].mesh[2] / param.kF) + push!(s_iw0s, s_iw[idx_iw0, :]) + push!(si_iw0s, si_iw[idx_iw0, :]) + end + println(length(s)) + + # DLR cutoffs + kF = param.kF + Euv, rtol = 1000 * param.EF, 1e-11 + maxK, minK = 20kF, 1e-8kF + Nk, order = 12, 8 + + # G0W0 + meff_g0w = SelfEnergy.massratio(param, s[1], si[1], δK)[1] + zfactor_g0w = SelfEnergy.zfactor(param, s[1]; ngrid=[-1, 0])[1] + # s0, si0 = SelfEnergy.G0W0( + # param; + # Euv=Euv, + # rtol=rtol, + # Nk=Nk, + # maxK=maxK, + # minK=minK, + # order=order, + # int_type=int_type, + # # Fs=int_type == :ko_const_p ? -Fs : -0.0, # NOTE: NEFT uses opposite sign convention for F! + # # Fa=int_type == :ko_const_pm ? -Fa : -0.0, # NOTE: NEFT uses opposite sign convention for F! + # ) + # meff_g0w = SelfEnergy.massratio(param, s0, si0, δK)[1] + # zfactor_g0w = SelfEnergy.zfactor(param, s0; ngrid=[-1, 0])[1] + + # GW0 + meff_gw = SelfEnergy.massratio(param, s[end], si[end], δK)[1] + zfactor_gw = SelfEnergy.zfactor(param, s[end]; ngrid=[-1, 0])[1] + + # Plot the real and imaginary parts of the static self-energy + fig, ax = plt.subplots(; nrows=2, sharex=true) + fig.set_figheight(6) + fig.set_figwidth(6) + colors = reverse(hex.((sequential_palette(0, length(s); s=100)))) + for j in eachindex(s) + if j == length(s) - 1 + plot_mvsrs(kkfs[j], real(s_iw0s[j]), "limegreen", "\$N_\\text{iter} = $n_max\$"; zorder=1000, lw=2, ax=ax[1]) + plot_mvsrs(kkfs[j], imag(s_iw0s[j]), "limegreen", ""; zorder=1000, lw=2, ax=ax[2]) + # ax[1].plot(kkfs[j], real(s_iw0s[j]); color="limegreen", lw=2, label="\$N_\\text{iter} = $n_max\$", zorder=1000) + # ax[2].plot(kkfs[j], imag(s_iw0s[j]); color="limegreen", lw=2, zorder=1000) + else + plot_mvsrs(kkfs[j], real(s_iw0s[j]), "#$(colors[j])", ""; ax=ax[1]) + plot_mvsrs(kkfs[j], imag(s_iw0s[j]), "#$(colors[j])", ""; ax=ax[2]) + # ax[1].plot(kkfs[j], real(s_iw0s[j]); color="#$(colors[j])") + # ax[2].plot(kkfs[j], imag(s_iw0s[j]); color="#$(colors[j])") + end + end + + ax[1].annotate( + # "\$r_s = $(rs)\$", + "\$r_s = $(Int(rs))\$", + # xy=(0.775, 0.225), + # xy=(0.8, 0.225), + xy=(0.786, 0.225), + xycoords="axes fraction", + ha="center", + va="center", + ) + ax[2].annotate( + "\$\\left(\\frac{m^*}{m}\\right)_{G_0 $wstring} = $(round(meff_g0w; sigdigits=4))\$", + xy=(0.737, 0.7), + # xy=(0.75, 0.75), + xycoords="axes fraction", + ha="center", + va="center", + ) + ax[2].annotate( + "\$\\left(\\frac{m^*}{m}\\right)_{G $wstring} = $(round(meff_gw; sigdigits=4))\$", + xy=(0.757, 0.55), + # xy=(0.757, 0.6), + xycoords="axes fraction", + ha="center", + va="center", + ) + ax[2].annotate( + "\$Z_{G_0 $wstring} = $(round(zfactor_g0w; sigdigits=4))\$", + xy=(0.783, 0.4), + # xy=(0.783, 0.45), + xycoords="axes fraction", + ha="center", + va="center", + ) + ax[2].annotate( + "\$Z_{G $wstring} = $(round(zfactor_gw; sigdigits=4))\$", + xy=(0.79, 0.25), + # xy=(0.79, 0.3), + xycoords="axes fraction", + ha="center", + va="center", + ) + + # ax[1].set_ylim(-0.35, 0.25) + # ax[1].set_yticks(-0.3:0.1:0.2) + ax[1].set_xlim(0, 5) + ax[2].set_xlim(0, 5) + ax[1].legend(loc="best") + # ax[2].legend(loc="best") + ax[1].set_ylabel("\$\\text{Re}\\Sigma_c(k, i\\omega_0)\$") + ax[2].set_ylabel("\$\\text{Im}\\Sigma_c(k, i\\omega_0)\$") + ax[2].set_xlabel("\$k / k_F\$") + plt.tight_layout() + fig.savefig("figures/static_gw_self_energy_$(int_type)_rs$(rs).pdf") +end + +main() diff --git a/example/sigma/sigma_MC.jl b/example/sigma/sigma_MC.jl index dcfdf7c..2b4f971 100644 --- a/example/sigma/sigma_MC.jl +++ b/example/sigma/sigma_MC.jl @@ -30,13 +30,7 @@ for (_rs, _mass2, _F, _beta, _order) in Iterators.product(rs, mass2, Fs, beta, o error("unknown mission") end - if isLayered2D - filename = "./data$(dim)d/data_$(mission)_layered2d.jld2" - else - filename = "./data$(dim)d/data_$(mission).jld2" - end - # filename = "data$(dim)_$(mission).jld2" - + filename = mission == "Z" ? sigma_z_filename : sigma_k_filename sigma, result = Sigma.MC(para; kgrid=kgrid, ngrid=ngrid, spinPolarPara=spinPolarPara, neval=neval, filename=filename, isLayered2D=isLayered2D, diff --git a/example/vertex4/plot_Fl.jl b/example/vertex4/plot_Fl.jl index e74df79..18c7e99 100644 --- a/example/vertex4/plot_Fl.jl +++ b/example/vertex4/plot_Fl.jl @@ -12,7 +12,7 @@ mass2 = [1.0, 1.5, 2.0, 2.2, 2.4, 2.5, 2.6, 2.8, 3.0, 3.5, 4.0, 4.5, 5.0, 6.0, 7 Fs = [-0.0,] beta = [25.0] order = [3,] -const fileName = symmetry ? "Fsl_$(dim)d.dat" : "Fal_$(dim)d.dat" +const filename = symmetry ? "Fsl_$(dim)d.dat" : "Fal_$(dim)d.dat" cdict = Dict(["blue" => "#0077BB", "cyan" => "#33BBEE", "teal" => "#009988", "orange" => "#EE7733", "red" => "#CC3311", "magenta" => "#EE3377", "grey" => "#BBBBBB"]); @@ -74,7 +74,7 @@ end if abspath(PROGRAM_FILE) == @__FILE__ - ver4_data = readdlm(fileName) + ver4_data = readdlm(filename) num_data = size(ver4_data)[1] for _l in ells diff --git a/src/para_wn_1minus0.csv b/src/para_wn_1minus0.csv index e5a9490..e8bc364 100644 --- a/src/para_wn_1minus0.csv +++ b/src/para_wn_1minus0.csv @@ -1719,6 +1719,266 @@ Fa,Fs,beta,dim,isDynamic,isFock,mass2,massratio,order,partition,rs,spin,Σw,Σw. -0.0,-0.0,25.0,3,false,false,3.0,1.0,4,220,1.0,1,-0.0011614872531492595,1.2868020343317447e-5,-0.0028097133416113114,7.87676337807096e-5 -0.0,-0.0,25.0,3,false,false,3.0,1.0,4,301,1.0,1,-0.020109024135336648,8.540916026771407e-6,0.00730458203271535,2.768525082278259e-5 -0.0,-0.0,25.0,3,false,false,3.0,1.0,4,100,1.0,1,0.0,5.092514679502708e-11,0.39941750806482884,0.00013769545527267605 +-0.0,-0.0,40.0,3,false,false,1.0,1.0,4,121,0.5,2,0.0,7.502635967975883e-12,3.060038074252017e-5,4.333818714507214e-6 +-0.0,-0.0,40.0,3,false,false,1.0,1.0,4,400,0.5,2,0.9968486444377477,0.0008833470986460412,0.2275736791076946,0.001786813758839584 +-0.0,-0.0,40.0,3,false,false,1.0,1.0,4,102,0.5,2,0.0,7.502635967975883e-12,0.10460995238956804,5.512371139361182e-5 +-0.0,-0.0,40.0,3,false,false,1.0,1.0,4,110,0.5,2,0.0,7.502635967975883e-12,0.16959857816092774,8.582425670291938e-5 +-0.0,-0.0,40.0,3,false,false,1.0,1.0,4,200,0.5,2,0.11260733877820966,4.9212727198908026e-5,0.44528554943722715,0.0004172281291781173 +-0.0,-0.0,40.0,3,false,false,1.0,1.0,4,112,0.5,2,0.0,7.502635967975883e-12,0.02045030283534831,1.0825539199233567e-5 +-0.0,-0.0,40.0,3,false,false,1.0,1.0,4,202,0.5,2,0.1229608817160322,4.9326910901684066e-5,0.09538652732755076,0.00012137713639625943 +-0.0,-0.0,40.0,3,false,false,1.0,1.0,4,210,0.5,2,0.004351454915060494,1.911286167756648e-5,-0.025279733119311816,0.0001327474500565992 +-0.0,-0.0,40.0,3,false,false,1.0,1.0,4,101,0.5,2,0.0,7.502635967975883e-12,0.2895113071658929,0.00015515429166939132 +-0.0,-0.0,40.0,3,false,false,1.0,1.0,4,300,0.5,2,-0.3117580862512242,0.00045824640605500255,-0.095065912400214,0.0006263114173182033 +-0.0,-0.0,40.0,3,false,false,1.0,1.0,4,120,0.5,2,0.0,7.502635967975883e-12,0.0007246644588140178,2.2798129109951535e-5 +-0.0,-0.0,40.0,3,false,false,1.0,1.0,4,201,0.5,2,0.12264000167099391,4.963966983623887e-5,0.1748218924968652,0.00018612599740078868 +-0.0,-0.0,40.0,3,false,false,1.0,1.0,4,310,0.5,2,-0.03126756297361464,0.0001292303063028889,0.07400668141308733,0.00045234952801025607 +-0.0,-0.0,40.0,3,false,false,1.0,1.0,4,111,0.5,2,0.0,7.502635967975883e-12,0.040511446066510415,2.0716470854249416e-5 +-0.0,-0.0,40.0,3,false,false,1.0,1.0,4,103,0.5,2,0.0,7.502635967975883e-12,0.055650045631915654,3.001993322647126e-5 +-0.0,-0.0,40.0,3,false,false,1.0,1.0,4,130,0.5,2,0.0,7.502635967975883e-12,-0.00022589398017537258,1.3943525151518148e-5 +-0.0,-0.0,40.0,3,false,false,1.0,1.0,4,211,0.5,2,0.004434639602875663,1.7806826421200704e-5,-0.051499613456998196,7.989232081829657e-5 +-0.0,-0.0,40.0,3,false,false,1.0,1.0,4,220,0.5,2,-0.0021061462893827146,1.3841573677006024e-5,-0.004078300263290344,9.893488612799421e-5 +-0.0,-0.0,40.0,3,false,false,1.0,1.0,4,301,0.5,2,-0.645585021551031,0.0009373216664267869,-0.1712107732921362,0.0007954850794215989 +-0.0,-0.0,40.0,3,false,false,1.0,1.0,4,100,0.5,2,0.0,7.502635967975883e-12,1.6972415332838082,0.0008033584869385905 +-0.0,-0.0,40.0,3,false,false,1.5,1.0,4,121,0.5,2,0.0,7.502635967975883e-12,2.7104697192932276e-5,4.255397760083627e-6 +-0.0,-0.0,40.0,3,false,false,1.5,1.0,4,400,0.5,2,0.28405439805654437,0.0002907303964726806,0.08293447967465231,0.0007977612462989534 +-0.0,-0.0,40.0,3,false,false,1.5,1.0,4,102,0.5,2,0.0,7.502635967975883e-12,0.12260679649404782,6.0683137005285495e-5 +-0.0,-0.0,40.0,3,false,false,1.5,1.0,4,110,0.5,2,0.0,7.502635967975883e-12,0.1531298464571048,7.392478697157487e-5 +-0.0,-0.0,40.0,3,false,false,1.5,1.0,4,200,0.5,2,0.07192369061720146,3.07073625400662e-5,0.37585446986446713,0.00032014316034832403 +-0.0,-0.0,40.0,3,false,false,1.5,1.0,4,112,0.5,2,0.0,7.502635967975883e-12,0.02053726129308617,1.0242193518032226e-5 +-0.0,-0.0,40.0,3,false,false,1.5,1.0,4,202,0.5,2,0.08260025366981918,3.1478923225397294e-5,0.09447982411370488,0.00010594003271886912 +-0.0,-0.0,40.0,3,false,false,1.5,1.0,4,210,0.5,2,0.0028471526499387043,1.190600544051889e-5,-0.008994923045906787,9.839332550640378e-5 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return @. (imag(data[nids[2], kidx]) - imag(data[nids[1], kidx])) / (2π / β) end +function zfactor_inverse_single(data, β, nidx=1, kidx=1) #assume the data are calculated with ngrid = [0], kgrid = [para.kF] + return @. imag(data[nidx, kidx]) / (π / β) +end + function meff_inverse(data, para, kgrid, i_dk=1, nidx=1) kF_label = searchsortedfirst(kgrid, para.kF) return @. (data[nidx, kF_label+i_dk] - data[nidx, kF_label-i_dk]) / (kgrid[kF_label+i_dk] - kgrid[kF_label-i_dk]) * para.me / para.kF @@ -37,20 +41,32 @@ function get_dzmu(para, datatuple; verbose=0, ngrid, kgrid, data = datatuple printstyled(UEG.short(para), color=:yellow) println() + @assert kgrid == [para.kF] "Function `get_dzmu` only supports kgrid = [para.kF]!" + @assert ngrid ∈ [[-1, 0], [0]] "Function `get_dzmu` only supports ngrid = [-1, 0] or [0]!" + + # Assumes the data are calculated with ngrid = [0], kgrid = [para.kF] or with ngrid = [-1, 0], kgrid = [para.kF] + p1 = first(keys(data)) + if size(data[p1], 1) == 1 + get_zfactor = (data, β) -> zfactor_inverse_single(data, β) + get_mu = data -> mu(data, 1, 1) + else + get_zfactor = (data, β) -> zfactor_inverse(data, β) + get_mu = data -> mu(data) + end if verbose > 0 for p in sort([k for k in keys(data)]) - println("$p: μ = $(mu(data[p])) z_inverse = $(zfactor_inverse(data[p], para.β))") + println("$p: μ = $(get_mu(data[p])) z_inverse = $(get_zfactor(data[p], para.β))") end end _mu = Dict() for (p, val) in data - _mu[p] = mu(val) + _mu[p] = get_mu(val) end _zinv = Dict() for (p, val) in data - _zinv[p] = zfactor_inverse(val, para.β) + _zinv[p] = get_zfactor(val, para.β) end dzinv, dmu, dz = CounterTerm.sigmaCT(para.order, _mu, _zinv) @@ -92,7 +108,7 @@ function getSigma(para, filename=filename; parafile="para_wn_1minus0.csv", root_ return ngrid, kgrid, rSw_k, iSw_k end -function getZfactor(para; parafile="para_wn_1minus0.csv", root_dir=@__DIR__, isRenorm=true) +function getZfactor(para; parafile="para_wn_1minus0.csv", root_dir=@__DIR__, isRenorm=false) _mu, _zinv = CounterTerm.getSigma(para, parafile=parafile, root_dir=root_dir) dzinv, dmu, dz = CounterTerm.sigmaCT(para.order, _mu, _zinv) @@ -105,6 +121,98 @@ function getZfactor(para; parafile="para_wn_1minus0.csv", root_dir=@__DIR__, isR end end +# 1/z = 1 - δs +function getZinv(para; parafile="para_wn_1minus0.csv", root_dir=@__DIR__) + _mu, _zinv = CounterTerm.getSigma(para, parafile=parafile, root_dir=root_dir) + dzinv, dmu, dz = CounterTerm.sigmaCT(para.order, _mu, _zinv) + sumzinv = accumulate(+, dzinv) + return @. 1.0 + sumzinv +end + +# ϵ_qp/ϵ_0 = 1 + δm +function getDispersionRatio(para, filename, idx_dk::Int=1; parafile="para_wn_1minus0.csv", root_dir=@__DIR__) + order = para.order + ngrid, kgrid, rdata, idata = loaddata(para, filename) + _Meffinv = Dict() + for (p, val) in rdata + _Meffinv[p] = -meff_inverse(val, para, kgrid, idx_dk) # δm + end + + dMeffinv, dmu, _dMeff = CounterTerm.sigmaCT(order, _mu, _Meffinv) + println("dMeffinv: ", dMeffinv) + sumMeffinv = accumulate(+, dMeffinv) + return @. 1.0 + sumMeffinv +end +function getDispersionRatio(para, rSigma, kgrid::Vector{Float64}; parafile="para_wn_1minus0.csv", root_dir=@__DIR__) + order, kF = para.order, para.kF + + # fit ReΣ(k,ω0) = a*(k-kF) + b*(k-kF)^2 + dMeffinv = [] + x = kgrid + @. model(x, p) = p[1] + p[2] * (x - kF) + p[3] * (x - kF)^2 + println(rSigma) + fit_parameters = [] + for o in 1:order + y = vec(Measurements.value.(rSigma[o])) + wt = vec(1 ./ Measurements.uncertainty.(rSigma[o]) .^ 2) + fit = curve_fit(model, x, y, wt, [1.0, -0.1, 0.0]) + push!(dMeffinv, -Measurements.measurement(coef(fit)[2], stderror(fit)[2]) * para.me / kF) + push!(fit_parameters, [coef(fit), stderror(fit)]) + end + + println("dMeffinv: ", dMeffinv) + sumMeffinv = accumulate(+, dMeffinv) + return @. 1.0 + sumMeffinv, fit_parameters +end + +# ϵ_0/ϵ_qp = 1 / (1 + δm) +function getDispersionRatioInv(para, filename, idx_dk::Int=1; parafile="para_wn_1minus0.csv", root_dir=@__DIR__) + order = para.order + ngrid, kgrid, rdata, idata = loaddata(para, filename) + _Meffinv = Dict() + for (p, val) in rdata + _Meffinv[p] = -meff_inverse(val, para, kgrid, idx_dk) + end + + _mu, _zinv = CounterTerm.getSigma(para, parafile=parafile, root_dir=root_dir) + + dMeffinv, dmu, _dMeff = CounterTerm.sigmaCT(order, _mu, _Meffinv) + println("dMeffinv: ", dMeffinv) + + println("_dMeff: ", _dMeff) + + Meff = Taylor1([1.0, _dMeff...], order) + dMeff = [getcoeff(Meff, o) for o in 1:order] + + sumMeff = accumulate(+, dMeff) + return @. 1.0 + sumMeff +end +function getDispersionRatioInv(para, rSigma, kgrid::Vector{Float64}; parafile="para_wn_1minus0.csv", root_dir=@__DIR__) + order, kF = para.order, para.kF + + # fit ReΣ(k,ω0) = a*(k-kF) + b*(k-kF)^2 + dMeffinv = [] + x = kgrid + @. model(x, p) = p[1] + p[2] * (x - kF) + p[3] * (x - kF)^2 + println(rSigma) + fit_parameters = [] + for o in 1:order + y = vec(Measurements.value.(rSigma[o])) + wt = vec(1 ./ Measurements.uncertainty.(rSigma[o]) .^ 2) + fit = curve_fit(model, x, y, wt, [1.0, -0.1, 0.0]) + push!(dMeffinv, -Measurements.measurement(coef(fit)[2], stderror(fit)[2]) * para.me / kF) + push!(fit_parameters, [coef(fit), stderror(fit)]) + end + + _Meffinv = Taylor1([1.0, dMeffinv...], order) + println(_Meffinv) + Meff = 1.0 / _Meffinv + dMeff = [getcoeff(Meff, o) for o in 1:order] + + sumMeff = accumulate(+, dMeff) + return @. 1.0 + sumMeff, fit_parameters +end + function getMeff(para, filename, idx_dk::Int=1; parafile="para_wn_1minus0.csv", root_dir=@__DIR__) order = para.order ngrid, kgrid, rdata, idata = loaddata(para, filename) @@ -123,14 +231,14 @@ function getMeff(para, filename, idx_dk::Int=1; parafile="para_wn_1minus0.csv", println("_dMeff: ", _dMeff) zinv = Taylor1([1.0, dzinv...], order) + inverse_dispersion_ratio = Taylor1([1.0, _dMeff...], order) - Meff = zinv * Taylor1([1.0, _dMeff...], order) + Meff = zinv * inverse_dispersion_ratio dMeff = [getcoeff(Meff, o) for o in 1:order] sumMeff = accumulate(+, dMeff) return @. 1.0 + sumMeff end - function getMeff(para, rSigma, kgrid::Vector{Float64}; parafile="para_wn_1minus0.csv", root_dir=@__DIR__) order, kF = para.order, para.kF @@ -155,12 +263,74 @@ function getMeff(para, rSigma, kgrid::Vector{Float64}; parafile="para_wn_1minus0 zinv = Taylor1([1.0, dzinv...], order) println(zinv) - _Meffinv = Taylor1([1.0, dMeffinv...], order) - println(_Meffinv) - Meff = zinv / _Meffinv + dispersion_ratio = Taylor1([1.0, dMeffinv...], order) + println(dispersion_ratio) + Meff = zinv / dispersion_ratio dMeff = [getcoeff(Meff, o) for o in 1:order] sumMeff = accumulate(+, dMeff) return @. 1.0 + sumMeff, fit_parameters # return @. 1.0 + sumMeff -end \ No newline at end of file +end + +function getMeffInv(para, filename, idx_dk::Int=1; parafile="para_wn_1minus0.csv", root_dir=@__DIR__) + order = para.order + ngrid, kgrid, rdata, idata = loaddata(para, filename) + _Meffinv = Dict() + for (p, val) in rdata + _Meffinv[p] = -meff_inverse(val, para, kgrid, idx_dk) + end + + _mu, _zinv = CounterTerm.getSigma(para, parafile=parafile, root_dir=root_dir) + + dzinv, dmu, dz = CounterTerm.sigmaCT(order, _mu, _zinv) + println("dmu: ", dmu) + + _dMeffinv, dmu, _dMeff = CounterTerm.sigmaCT(order, _mu, _Meffinv) + println("dMeffinv: ", _dMeffinv) + + println("_dMeff: ", _dMeff) + zfactor = Taylor1([1.0, dz...], order) + dispersion_ratio = Taylor1([1.0, _dMeffinv...], order) + + MeffInv = zfactor * dispersion_ratio + dMeffInv = [getcoeff(MeffInv, o) for o in 1:order] + + sumMeffInv = accumulate(+, dMeffInv) + return @. 1.0 + sumMeffInv +end +function getMeffInv(para, rSigma, kgrid::Vector{Float64}; parafile="para_wn_1minus0.csv", root_dir=@__DIR__) + order, kF = para.order, para.kF + + # fit ReΣ(k,ω0) = a*(k-kF) + b*(k-kF)^2 + dMeffinv = [] + x = kgrid + @. model(x, p) = p[1] + p[2] * (x - kF) + p[3] * (x - kF)^2 + println(rSigma) + fit_parameters = [] + for o in 1:order + y = vec(Measurements.value.(rSigma[o])) + wt = vec(1 ./ Measurements.uncertainty.(rSigma[o]) .^ 2) + fit = curve_fit(model, x, y, wt, [1.0, -0.1, 0.0]) + push!(dMeffinv, -Measurements.measurement(coef(fit)[2], stderror(fit)[2]) * para.me / kF) + push!(fit_parameters, [coef(fit), stderror(fit)]) + end + + # para1 = ParaMC(rs=para.rs, beta=40.0, Fs=para.Fs, order=para.order, mass2=para.mass2, isDynamic=para.isDynamic, dim=para.dim, spin=para.spin) + # _mu, _zinv = CounterTerm.getSigma(para1, parafile=parafile, root_dir=root_dir) + _mu, _zinv = CounterTerm.getSigma(para, parafile=parafile, root_dir=root_dir) + dzinv, dmu, dz = CounterTerm.sigmaCT(para.order, _mu, _zinv) + zfactor = Taylor1([1.0, dz...], order) + zinv = Taylor1([1.0, dz...], order) + println("z: ", zfactor) + println("1/zinv: ", 1.0 / zinv) + + dispersion_ratio = Taylor1([1.0, dMeffinv...], order) + println(dispersion_ratio) + + MeffInv = zfactor * dispersion_ratio + dMeffInv = [getcoeff(MeffInv, o) for o in 1:order] + + sumMeffInv = accumulate(+, dMeffInv) + return @. 1.0 + sumMeffInv, fit_parameters +end