Parallelized DMRG

Basic installations

First install julia or make sure you got Julia version 1.10 or higher:

curl -fsSL https://install.julialang.org | sh

Then create environment

cd ~
mkdir julia; cd julia
julia
]
activate DMRGenv
add HDF5 LinearAlgebra Strided Dates Random InteractiveUtils DelimitedFiles Plots Printf ITensors ITensorMPS MPIPreferences MPI

Go back to the Julia REPL with backspace

exit()
mkdir ITensorParallel
cd ITensorParallel
git clone https://github.com/ITensor/ITensorParallel.jl.git
cd ..
julia
]
activate DMRGenv

Go back to Julia REPL with backspace

using Pkg;    Pkg.develop(path="./ITensorParallel/ITensorParallel.jl");    using ITensorParallel
]
precompile
instantiate

If you want to use the environment, run from now on:

julia --project=~/julia/DMRGenv script.jl

where after the equal sign you add the path to your environment.

Now, also make sure that you installed a version of MPI. The path to the mpi lib folder should be added to the ~/.bashrc or ~/.zshrc file on Linux / MacOS respectively.

How to use the code

DMRG

Command

cd src
mkdir parent_calc_folder
mpirun -n <n> julia --project=~/path-to-env \
DMRG_template_pll_Energyextrema.jl <s> <N> <J> [Sz] \
<nexc> <conserve_symmetry> <print_HDF5> <maximal_energy>\
> parent_calc_folder/dmrg.out 2> parent_calc_folder/dmrg.err

or via an input file containing all the arguments:

mpirun -n <n> julia --project=~/path-to-env \
DMRG_template_pll_Energyextrema.jl < dmrg.inp \
> parent_calc_folder/dmrg.out 2> parent_calc_folder/dmrg.err

Arguments

n [Int]: Number of MPI-processes, usually something between 2 and 16 is optimal, depending on the system size.
s [Int] or [Int/2]: S quantum number of every Spin in the chain
N [Int]: length of the spinchain
J [Float64] or [Matrix{Float64}] of size N x N: Value / matrix containing all the J values for the Heisenberg term of the Hamiltonian
Sz [Int] or [Int/2]: QN defining the sum of the sum of the local sz QN over the whole chain. This parameter is only important if conserve_symmetryis set to true, else Sz gets automatically set to nothing. It is therefore also only necessary if you want to conserve symmetry.
nexc [Int]: Defines the number of excited states which are calculated. If you only want the ground state, set it to 0.
conserve_symmetry [Bool]: Defines if the sz QN should be symmetric over the whole chain.
print_HDF5 [Bool]: Defines if you want to print the HDF5 representations for the Hamiltonian, the Wavefuncitons, and information about the sites. This argument has to be set to true if you want to do a dynamical correlator calculation afterwards.
maximal_energy [Bool]: Defines if the maximal energy of the system should be calculated. This argument has to be set to true if you want to do a dynamical correlator calculation afterwards.

Outputs

The script outputs an array of energy values for all calculated states of the hamiltonian. In addition, it prints the arrays for <ψn|S²|ψn> and <ψn|Sz(i)|ψn>, where ψn are all the calculated wave functions. If specified, it outputs the HDF5 files of the wavefunction MPS, the hamiltonian MPO and the sites information.

Example

mpirun -n 4 julia --project=~/julia/DMRGenv \
DMRG_template_pll_Energyextrema.jl 0.5 10 0.4 0 1 true \
true true > parent_calc_folder/dmrg.out 2> parent_calc_folder/dmrg.err

Dynamical Correlator

Command

First, make sure, that you copy all created HDF5 files into the folder parent_calc_folder

cp *.h5 parent_calc_folder/

julia -t <t> --project=/path-to-env Dynam_Corr.jl <J> [N] [cutoff] \ 
> dyncorr.out 2> dyncorr.err

or with an input file:

julia -t <t> --project=/path-to-env Dynam_Corr.jl < dyncorr.inp \
> dyncorr.out 2> dyncorr.err

Arguments

t [Int]: Specifies the number of threads for the script. Here more than the number of sites is not necessary.
J [Float64] or [Matrix{Float64}] of size N x N: Value / matrix containing all the J values for the Heisenberg term of the Hamiltonian. This term has to be the same as for the preceding DMRG calculation.
N [Int]: Specifies the number of chebyshev expansion coefficients. If no N is specified, the default value of max(W, 600) is taken, where W is the effective bandwidth of the hamiltonian, i.e. the difference between the minimal and maximal energy.
cutoff [Float64]: Defines the cutoff value for the add function of MPOs. The bigger the value, the faster but the more inaccurate the calculation is. This value is by default set to 1e-8. A reasonable range of cutoff values is between 1e-8 and 1e-6.

From the arguments N and cutoff none, one or both can be provided. The order of these two does not matter.

Outputs

This script outputs the dynamical correlator for ω values between 0 and 2 J_mean for all sites of the spinchain. J_mean is J, if J is a float and the mean of the non-zero values of J if J is a matrix. Additionally, it already creates a normalized plot of the values.

Example

julia -t 5 --project=~/julia/DMRGenv Dynam_Corr.jl 0.4 1000 1e-6 > \
dyncorr.out 2> dyncorr.err

AiiDA workchain

The DMRG code can be used via an AiiDAlab workchain.

verdi code create core.code.installed --label dmrg --computer localhost --filepath-executable /home/jovyan/Bachelor-Arbeit/src/DMRG_template_pll_Energyextrema.jl --non-interactive
verdi code list 
git clone https://github.com/grafrap/aiida-dmrg.git
cd aiida-dmrg 
pip install --user -e .
verdi plugin list aiida.calculations
verdi computer setup --config daint-mc-julia.yaml
verdi code setup --config dmrg.yaml
verdi code setup --config dyncorr.yaml

Further information how to use the workchain can be found in the Readme of the aiida-dmrg git repository.