solutions_toycodes.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "id": "2fe29049",
   "metadata": {},
   "source": [
    "# Solutions for the `exercise_toycodes.ipynb` notebook"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "39301469",
   "metadata": {},
   "source": [
    "Uncomment and run the cells below (removing the `#`) when running this notebook on https://colab.research.google.com.\n",
    "\n",
    "Alternatively, you can run this notebook locally with jupyter, provided that you have the `toycodes` subfolder from \n",
    "https://github.com/tenpy/tenpy_toycodes\n",
    "in the same folder as your notebook."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "id": "8d42e939",
   "metadata": {},
   "outputs": [],
   "source": [
    "#!pip install git+https://github.com/tenpy/tenpy_toycodes.git\n",
    "\n",
    "# use `pip uninstall tenpy-toycodes` to remove it a gain."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "e7d5c720",
   "metadata": {},
   "source": [
    "This tutorial focuses on a set of toy codes (using only python with numpy + scipy) that provide a simple implementation of the various MPS algorithms.\n",
    "\n",
    "You can add your code below by inserting additional cells as neccessary and running them (press Shift+Enter).\n",
    "\n",
    "**DISCLAIMER**: the toy codes used are not optimized, and we only use very small bond dimensions here. For state-of-the-art MPS calculations (especially for cylinders towards 2D), `chi` should be significantly larger, often on the order of several 1000s."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "56956a97",
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "id": "b7d6aedd",
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "import scipy\n",
    "import matplotlib.pyplot as plt\n",
    "\n",
    "np.set_printoptions(precision=5, suppress=True, linewidth=100)\n",
    "plt.rcParams['figure.dpi'] = 150"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "337e0452",
   "metadata": {},
   "source": [
    "## toy codes: a_mps.py\n",
    "\n",
    "The file [a_mps.py](https://github.com/tenpy/tenpy_toycodes/blob/main/tenpy_toycodes/a_mps.py) defines a `SimpleMPS` class, that provides methods for expectation values and the entanglement entropy. You can initialize an inital product state MPS with the provided functions `init_FM_MPS` or `init_Neel_MPS`:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "id": "8b2cfaee",
   "metadata": {},
   "outputs": [],
   "source": [
    "from tenpy_toycodes.a_mps import init_FM_MPS, init_Neel_MPS, SimpleMPS"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "id": "a4f0ecc0",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "<tenpy_toycodes.a_mps.SimpleMPS object at 0x7f966247bee0>\n",
      "[1. 1. 1. 1. 1. 1. 1. 1. 1. 1.]\n"
     ]
    }
   ],
   "source": [
    "psi_FM = init_FM_MPS(L=10, d=2, bc='finite')\n",
    "print(psi_FM)\n",
    "SigmaZ = np.diag([1., -1.])\n",
    "print(psi_FM.site_expectation_value(SigmaZ))"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "8b77ba98",
   "metadata": {},
   "source": [
    "### Exercise\n",
    "Initialize a Neel state MPS. Print the `SigmaZ` expectation values.\n",
    "\n",
    "\n",
    "Print the entanglement entropy. What do you expect? Why do you get so many numbers, and not just one?\n",
    "Tipp: read the code ;-)\n",
    "\n",
    "Extract the half-chain entanglement entropy, i.e., the entropy when cutting the chain into two equal-length halves."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "id": "667882c2",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[ 1. -1.  1. -1.  1. -1.  1. -1.  1. -1.]\n"
     ]
    }
   ],
   "source": [
    "psi_Neel = init_Neel_MPS(L=10, d=2, bc='finite')\n",
    "print(psi_Neel.site_expectation_value(SigmaZ))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "id": "9a255d8e",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[-0. -0. -0. -0. -0. -0. -0. -0. -0.]\n",
      "half-chain entropy:  -0.0\n"
     ]
    }
   ],
   "source": [
    "print(psi_Neel.entanglement_entropy())  # one for each bond!\n",
    "print(\"half-chain entropy: \", psi_Neel.entanglement_entropy()[(psi_Neel.L - 1)//2])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "7905b006-9232-437a-a3aa-ba75eb6bb96a",
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "markdown",
   "id": "fa01d6ed-36fd-4e7c-8a24-5d3197be1d2e",
   "metadata": {},
   "source": [
    "### Exercise\n",
    "\n",
    "Write a function to initialize an MPS representing a product of singlets on neighboring sites.\n",
    "Check the expectation values of $\\sigma^z$, entropies and the correlation functions $\\sigma^z_0 \\sigma^z_1$ and $\\sigma^z_0 \\sigma^z_2$ for correctness.\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "id": "a5c60fcb-6399-4985-90a8-ed441aad73ad",
   "metadata": {},
   "outputs": [],
   "source": [
    "def init_singlet_MPS(L, bc='finite'):\n",
    "    \"\"\"Return a Neel state MPS (= product state with alternating spins up  down up down... )\"\"\"\n",
    "    Bs = []\n",
    "    Ss = []\n",
    "    for i in range(L):\n",
    "        if i % 2 == 0:      \n",
    "            B = np.zeros([1, 2, 2], dtype=float)\n",
    "            B[0, 0, 1] = 0.5**0.5\n",
    "            B[0, 1, 0] = - 0.5**0.5\n",
    "            S = np.ones([1], dtype=float)\n",
    "        else:\n",
    "            B = np.zeros([2, 2, 1], dtype=float)\n",
    "            B[0, 0, 0] = 1.\n",
    "            B[1, 1, 0] = 1.\n",
    "            S = 0.5**0.5 * np.ones([2], dtype=float)\n",
    "        Bs.append(B)\n",
    "        Ss.append(S)\n",
    "    return SimpleMPS(Bs, Ss, bc=bc)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "id": "5b5ec318-5492-4aae-b377-fb47af4ab3d4",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[0. 0. 0. 0. 0. 0. 0. 0. 0. 0.]\n",
      "[ 0.69315 -0.       0.69315 -0.       0.69315 -0.       0.69315 -0.       0.69315]\n",
      "-1.0000000000000002\n",
      "0.0\n"
     ]
    }
   ],
   "source": [
    "psi_singlet = init_singlet_MPS(L=10, bc='finite')\n",
    "print(psi_singlet.site_expectation_value(SigmaZ))\n",
    "print(psi_singlet.entanglement_entropy())  # one for each bond!\n",
    "print(psi_singlet.correlation_function(SigmaZ, 0, SigmaZ, 1))\n",
    "print(psi_singlet.correlation_function(SigmaZ, 0, SigmaZ, 2))\n",
    "\n"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "0966eb59",
   "metadata": {},
   "source": [
    "## toy codes: b_model.py\n",
    "\n",
    "The file [b_model.py](https://github.com/tenpy/tenpy_toycodes/blob/main/tenpy_toycodes/b_model.py) defines a `TFIModel` class representing the transverse field Ising model        \n",
    "$$H = - J \\sum_{i} \\sigma^z_i \\sigma^z_{i+1} - g \\sum_{i} \\sigma^x_i$$\n",
    "\n",
    "\n",
    "that provides both in the form of bond-terms `H_bonds` (as required for TEBD) and in the form of an MPO `H_mpo`.\n",
    "You can use `H_bonds` with `SimpleMPS.bond_expectation_values` to evalue the energy.\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "id": "d439f112",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "<H_bonds> =  [-1. -1. -1. -1. -1. -1. -1. -1. -1.]\n",
      "energy: -9.0\n"
     ]
    }
   ],
   "source": [
    "from tenpy_toycodes.b_model import TFIModel\n",
    "\n",
    "model = TFIModel(L=10, J=1., g=1.2, bc='finite')\n",
    "\n",
    "print(\"<H_bonds> = \", psi_FM.bond_expectation_value(model.H_bonds))\n",
    "print(\"energy:\", np.sum(psi_FM.bond_expectation_value(model.H_bonds)))\n",
    "# (make sure the model and state have the same length and boundary conditions!)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "017d4d67",
   "metadata": {},
   "source": [
    "### Exercise\n",
    "\n",
    "Check the energies for the Neel state and make sure it matches what you expect."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "id": "d0ef22db",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "energy Neel: 9.0\n"
     ]
    }
   ],
   "source": [
    "E = sum(psi_Neel.bond_expectation_value(model.H_bonds))\n",
    "print(\"energy Neel:\", E)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "bd218561",
   "metadata": {},
   "source": [
    "## toy codes: c_tebd.py\n",
    "\n",
    "The file [c_tebd.py](https://github.com/tenpy/tenpy_toycodes/blob/main/tenpy_toycodes/c_tebd.py) implements the TEBD algorithm. \n",
    "\n",
    "You can run TEBD with imaginary time evolutinon to find the ground state like this:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "id": "d6c0d701",
   "metadata": {},
   "outputs": [],
   "source": [
    "from tenpy_toycodes.c_tebd import calc_U_bonds, run_TEBD"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "id": "2e8f7a57",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "dt = 0.10000: E = -13.8961677194781\n",
      "dt = 0.01000: E = -13.9426155514706\n",
      "dt = 0.00100: E = -13.9468077059314\n",
      "dt = 0.00010: E = -13.9472289924180\n",
      "dt = 0.00001: E = -13.9472711443175\n",
      "final bond dimensions:  [2, 4, 8, 14, 15, 14, 8, 4, 2]\n",
      "magnetization in X = 8.24005\n",
      "magnetization in Z = 0.01748\n"
     ]
    }
   ],
   "source": [
    "# assuming you defined a `model`\n",
    "\n",
    "chi_max = 15\n",
    "\n",
    "psi = init_FM_MPS(model.L, model.d, model.bc)\n",
    "for dt in [0.1, 0.01, 0.001, 1.e-4, 1.e-5]:\n",
    "    U_bonds = calc_U_bonds(model.H_bonds, dt)\n",
    "    run_TEBD(psi, U_bonds, N_steps=100, chi_max=chi_max, eps=1.e-10)\n",
    "    E = np.sum(psi.bond_expectation_value(model.H_bonds))\n",
    "    print(\"dt = {dt:.5f}: E = {E:.13f}\".format(dt=dt, E=E))\n",
    "# the `run_TEBD` modified `psi`, so we can now calculate the expectation values from it\n",
    "print(\"final bond dimensions: \", psi.get_chi())\n",
    "mag_x = np.sum(psi.site_expectation_value(model.sigmax))\n",
    "mag_z = np.sum(psi.site_expectation_value(model.sigmaz))\n",
    "print(\"magnetization in X = {mag_x:.5f}\".format(mag_x=mag_x))\n",
    "print(\"magnetization in Z = {mag_z:.5f}\".format(mag_z=mag_z))\n"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "a4785dbd-afd4-436b-ae11-178992509837",
   "metadata": {},
   "source": [
    "### Exercise\n",
    "\n",
    "Read the code of [c_tebd.py](https://github.com/tenpy/tenpy_toycodes/blob/main/tenpy_toycodes/c_tebd.py) and try to understand the general structure of how it works.\n"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "bb7b318b",
   "metadata": {},
   "source": [
    "## toy codes: d_dmrg.py\n",
    "\n",
    "The file [d_dmrg.py](https://github.com/tenpy/tenpy_toycodes/blob/main/tenpy_toycodes/d_dmrg.py) implements the DMRG algorithm.\n",
    "It can be called like this:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "id": "3196f562",
   "metadata": {},
   "outputs": [],
   "source": [
    "from tenpy_toycodes.d_dmrg import SimpleDMRGEngine, SimpleHeff2"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "id": "ffc67843",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "sweep  1: E = -13.9497659535850\n",
      "sweep  2: E = -13.9473400231317\n",
      "sweep  3: E = -13.9473400175491\n",
      "sweep  4: E = -13.9473400175491\n",
      "sweep  5: E = -13.9473400175491\n",
      "sweep  6: E = -13.9473400175491\n",
      "sweep  7: E = -13.9473400175491\n",
      "sweep  8: E = -13.9473400175491\n",
      "sweep  9: E = -13.9473400175491\n",
      "sweep 10: E = -13.9473400175491\n",
      "final bond dimensions:  [2, 4, 8, 14, 15, 14, 8, 4, 2]\n",
      "magnetization in X = 0.82406\n",
      "magnetization in Z = -0.00000\n"
     ]
    }
   ],
   "source": [
    "chi_max = 15\n",
    "\n",
    "psi = init_FM_MPS(model.L, model.d, model.bc)\n",
    "eng = SimpleDMRGEngine(psi, model, chi_max=chi_max, eps=1.e-10)\n",
    "for i in range(10):\n",
    "    E_dmrg = eng.sweep()\n",
    "    E = np.sum(psi.bond_expectation_value(model.H_bonds))\n",
    "    print(\"sweep {i:2d}: E = {E:.13f}\".format(i=i + 1, E=E))\n",
    "print(\"final bond dimensions: \", psi.get_chi())\n",
    "mag_x = np.mean(psi.site_expectation_value(model.sigmax))\n",
    "mag_z = np.mean(psi.site_expectation_value(model.sigmaz))\n",
    "print(\"magnetization in X = {mag_x:.5f}\".format(mag_x=mag_x))\n",
    "print(\"magnetization in Z = {mag_z:.5f}\".format(mag_z=mag_z))"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "b0eee6bf",
   "metadata": {},
   "source": [
    "### Exercise\n",
    "\n",
    "Read the code of [d_dmrg.py](https://github.com/tenpy/tenpy_toycodes/blob/main/tenpy_toycodes/d_dmrg.py) and try to understand the general structure of how it works.\n"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "dbd12c50",
   "metadata": {},
   "source": [
    "### Exercise\n",
    "\n",
    "Compare running the code cells for DMRG and imaginary time evolution TEBD abovce for various parameters \n",
    "of `L`, `J`, `g`, and `bc`. Which one is faster? Do they always agree?\n",
    "\n",
    "Note: \n",
    "The transverse field Ising model has a quantum phase transition at $g/J = 1.$,\n",
    "from a ferro-magnetic phase (`g < J `) to a paramagnetic phase (`g > J`). We will map out the full phase diagram below."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "id": "b4e7e445",
   "metadata": {},
   "outputs": [],
   "source": [
    "model = TFIModel(L=20, J=1., g=1.0, bc='finite')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "id": "cbf84fcc",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "sweep  1: E = -25.0832904523074\n",
      "sweep  2: E = -25.1078139618274\n",
      "sweep  3: E = -25.1077971116273\n",
      "sweep  4: E = -25.1077971116245\n",
      "sweep  5: E = -25.1077971116245\n",
      "sweep  6: E = -25.1077971116245\n",
      "sweep  7: E = -25.1077971116245\n",
      "sweep  8: E = -25.1077971116245\n",
      "sweep  9: E = -25.1077971116245\n",
      "sweep 10: E = -25.1077971116245\n",
      "final bond dimensions:  [2, 4, 8, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 8, 4, 2]\n",
      "magnetization in X = 0.69494\n",
      "magnetization in Z = -0.00000\n"
     ]
    }
   ],
   "source": [
    "chi_max = 15\n",
    "\n",
    "psi = init_FM_MPS(model.L, model.d, model.bc)\n",
    "eng = SimpleDMRGEngine(psi, model, chi_max=chi_max, eps=1.e-10)\n",
    "for i in range(10):\n",
    "    E_dmrg = eng.sweep()\n",
    "    E = np.sum(psi.bond_expectation_value(model.H_bonds))\n",
    "    print(\"sweep {i:2d}: E = {E:.13f}\".format(i=i + 1, E=E))\n",
    "print(\"final bond dimensions: \", psi.get_chi())\n",
    "mag_x = np.mean(psi.site_expectation_value(model.sigmax))\n",
    "mag_z = np.mean(psi.site_expectation_value(model.sigmaz))\n",
    "print(\"magnetization in X = {mag_x:.5f}\".format(mag_x=mag_x))\n",
    "print(\"magnetization in Z = {mag_z:.5f}\".format(mag_z=mag_z))"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "8717f6a4",
   "metadata": {},
   "source": [
    "## Infinite DMRG\n",
    "\n",
    "The `SimpleDMRG` code also allows to run infinite DMRG, simply by replacing the `bc='finite'` for both the model and the MPS. Look at the implementation of `d_dmrg.py` to see where the differences are.\n",
    "\n",
    "The `L` parameter now just indices the number of tensors insite the unit cell of the infinite MPS.\n",
    "It has to be at least `2`, since we optimize 2 tensors at once in our DMRG code.\n",
    "Further, note that we now use the `mean` to calculate densities of observables instead of extensive quantities (like L)."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "id": "76ab2cc8",
   "metadata": {},
   "outputs": [],
   "source": [
    "model = TFIModel(L=2, J=1., g=0.2, bc='infinite')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "id": "717abeee",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "sweep  1: E/L = -1.0257321728263\n",
      "sweep  2: E/L = -1.0101679578537\n",
      "sweep  3: E/L = -1.0100254885278\n",
      "sweep  4: E/L = -1.0100315048164\n",
      "sweep  5: E/L = -1.2804073779119\n",
      "sweep  6: E/L = -1.0104742300583\n",
      "sweep  7: E/L = -1.0100252539846\n",
      "sweep  8: E/L = -1.0100252539846\n",
      "sweep  9: E/L = -1.0100252539846\n",
      "sweep 10: E/L = -1.0100252539846\n",
      "final bond dimensions:  [3, 3]\n",
      "magnetization in X = 0.10051\n",
      "magnetization in Z = 0.99491\n"
     ]
    }
   ],
   "source": [
    "chi_max = 10\n",
    "\n",
    "psi = init_FM_MPS(model.L, model.d, model.bc)\n",
    "eng = SimpleDMRGEngine(psi, model, chi_max=chi_max, eps=1.e-7)\n",
    "for i in range(10):\n",
    "    E_dmrg = eng.sweep()\n",
    "    E = np.mean(psi.bond_expectation_value(model.H_bonds))\n",
    "    print(\"sweep {i:2d}: E/L = {E:.13f}\".format(i=i + 1, E=E))\n",
    "print(\"final bond dimensions: \", psi.get_chi())\n",
    "mag_x = np.mean(psi.site_expectation_value(model.sigmax))\n",
    "mag_z = np.mean(psi.site_expectation_value(model.sigmaz))\n",
    "print(\"magnetization in X = {mag_x:.5f}\".format(mag_x=mag_x))\n",
    "print(\"magnetization in Z = {mag_z:.5f}\".format(mag_z=mag_z))"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "1b260440",
   "metadata": {},
   "source": [
    "### Exercise\n",
    "\n",
    "Extend the following function `run_DMRG` to initialize an MPS compatible with the model, run DMRG on that MPS and return the corresponding state."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "id": "b76969aa",
   "metadata": {},
   "outputs": [],
   "source": [
    "def run_DMRG(model, chi_max=50):\n",
    "    print(f\"runnning DMRG for L={model.L:d}, g={model.g:.2f}, bc={model.bc}, chi_max={chi_max:d}\")\n",
    "    #raise NotImplementedError(\"TODO: this is an Exercise!\")\n",
    "    \n",
    "    psi = init_FM_MPS(model.L, model.d, model.bc)\n",
    "    eng = SimpleDMRGEngine(psi, model, chi_max=chi_max, eps=1.e-10)\n",
    "    for i in range(10):\n",
    "        eng.sweep()\n",
    "        E_bond = psi.bond_expectation_value(model.H_bonds)\n",
    "        if model.bc == 'finite': \n",
    "            E = np.sum(E_bond)\n",
    "        else:\n",
    "            E = np.mean(E_bond)\n",
    "        #print(\"sweep {i:2d}: E = {E:.13f}\".format(i=i + 1, E=E))\n",
    "    print(f\"max chi ={max(psi.get_chi())}\")\n",
    "    return psi"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "e9b9796c",
   "metadata": {},
   "source": [
    "### Exercise\n",
    "\n",
    "Use that function to check that the average energy density and expectation values for infinite DMRG are independent of the unit cell length `L`."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "id": "0f7df7fc",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "runnning DMRG for L=2, g=0.20, bc=infinite, chi_max=50\n",
      "max chi =6\n",
      "[-1.01003 -1.01003]\n",
      "\n",
      "\n",
      "runnning DMRG for L=4, g=0.20, bc=infinite, chi_max=50\n",
      "max chi =5\n",
      "[-1.01003 -1.01003 -1.01003 -1.01003]\n"
     ]
    }
   ],
   "source": [
    "model = TFIModel(L=2, J=1., g=0.2, bc='infinite')\n",
    "psi = run_DMRG(model)\n",
    "print(psi.bond_expectation_value(model.H_bonds))\n",
    "print(\"\\n\")\n",
    "model = TFIModel(L=4, J=1., g=0.2, bc='infinite')\n",
    "psi = run_DMRG(model)\n",
    "print(psi.bond_expectation_value(model.H_bonds))"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "8f7b39ac",
   "metadata": {},
   "source": [
    "### Exercise\n",
    "\n",
    "Use the `run_DMRG` function above to plot expectation values as a function of `g` for fixed `J=1` with the following code.\n",
    "\n",
    "\n",
    "Modify it to also plot the average expectation values of `sigmaz` and `sigmax` and the \n",
    "`sigmaz` correlation function between spin 0 and 20."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "id": "e9a35a7b",
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "runnning DMRG for L=2, g=0.00, bc=infinite, chi_max=50\n",
      "max chi =1\n",
      "runnning DMRG for L=2, g=0.10, bc=infinite, chi_max=50\n",
      "max chi =5\n",
      "runnning DMRG for L=2, g=0.20, bc=infinite, chi_max=50\n",
      "max chi =6\n",
      "runnning DMRG for L=2, g=0.30, bc=infinite, chi_max=50\n",
      "max chi =9\n",
      "runnning DMRG for L=2, g=0.40, bc=infinite, chi_max=50\n",
      "max chi =17\n",
      "runnning DMRG for L=2, g=0.50, bc=infinite, chi_max=50\n",
      "max chi =20\n",
      "runnning DMRG for L=2, g=0.60, bc=infinite, chi_max=50\n",
      "max chi =28\n",
      "runnning DMRG for L=2, g=0.70, bc=infinite, chi_max=50\n",
      "max chi =36\n",
      "runnning DMRG for L=2, g=0.80, bc=infinite, chi_max=50\n",
      "max chi =44\n",
      "runnning DMRG for L=2, g=0.90, bc=infinite, chi_max=50\n",
      "max chi =50\n",
      "runnning DMRG for L=2, g=1.00, bc=infinite, chi_max=50\n",
      "max chi =50\n",
      "runnning DMRG for L=2, g=1.10, bc=infinite, chi_max=50\n",
      "max chi =43\n",
      "runnning DMRG for L=2, g=1.20, bc=infinite, chi_max=50\n",
      "max chi =36\n",
      "runnning DMRG for L=2, g=1.30, bc=infinite, chi_max=50\n",
      "max chi =28\n",
      "runnning DMRG for L=2, g=1.40, bc=infinite, chi_max=50\n",
      "max chi =24\n",
      "runnning DMRG for L=2, g=1.50, bc=infinite, chi_max=50\n",
      "max chi =21\n",
      "runnning DMRG for L=2, g=1.60, bc=infinite, chi_max=50\n",
      "max chi =21\n",
      "runnning DMRG for L=2, g=1.70, bc=infinite, chi_max=50\n",
      "max chi =18\n",
      "runnning DMRG for L=2, g=1.80, bc=infinite, chi_max=50\n",
      "max chi =18\n",
      "runnning DMRG for L=2, g=1.90, bc=infinite, chi_max=50\n",
      "max chi =15\n",
      "runnning DMRG for L=2, g=2.00, bc=infinite, chi_max=50\n",
      "max chi =15\n"
     ]
    }
   ],
   "source": [
    "#gs = [0.1, 0.5, 1.0, 1.5, 2.0]\n",
    "gs = np.linspace(0., 2., 21)\n",
    "entropies = []\n",
    "vals_X = []\n",
    "vals_Z = []\n",
    "corrs_ZZ = []\n",
    "\n",
    "\n",
    "for g in gs:\n",
    "    model = TFIModel(L=2, J=1., g=g, bc='infinite')\n",
    "    psi = run_DMRG(model, chi_max=50)\n",
    "    entropies.append(np.max(psi.entanglement_entropy()))\n",
    "    vals_X.append(np.mean(psi.site_expectation_value(model.sigmax)))\n",
    "    vals_Z.append(np.mean(psi.site_expectation_value(model.sigmaz)))\n",
    "    corrs_ZZ.append(np.mean(psi.correlation_function(model.sigmaz, 0, model.sigmaz, 20)))\n",
    "\n",
    "    "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "id": "4ce49bc6",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.legend.Legend at 0x7f95f0186dd0>"
      ]
     },
     "execution_count": 22,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 960x720 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.plot(gs, entropies, marker='o', label='max entropy $S$')\n",
    "# plot expecation values of sigmax and sigmaz as well\n",
    "plt.plot(gs, vals_X, marker='+', label=r'$<\\sigma^x>$')\n",
    "plt.plot(gs, vals_Z, marker='x', label=r'$<\\sigma^z>$')\n",
    "plt.plot(gs, corrs_ZZ, marker='x', label=r'$<\\sigma^z_0 \\sigma^z_{20}>$')\n",
    "\n",
    "\n",
    "plt.xlabel('$g/J$')\n",
    "plt.ylabel('expectation values')\n",
    "plt.legend(loc='best')\n"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "17bee63e",
   "metadata": {},
   "source": [
    "## Defining a new model: the XX chain\n",
    "\n",
    "For the time evolution, we want to consider the XX chain in a staggered field, given by the Hamiltonian\n",
    "\n",
    "$$ H = \\sum_{i=0}^{N-2} (\\sigma^x_i \\sigma^x_{i+1} + \\sigma^y_i \\sigma^y_{i+1})  - h_s \\sum_{i=0}^{N-1} (-1)^i \\sigma^z_i \n",
    "     = 2 \\sum_{i=0}^{N-2} (\\sigma^+_i \\sigma^-_{i+1} + \\sigma^+_i \\sigma^-_{i+1})  - h_s \\sum_{i=0}^{N-1} (-1)^i \\sigma^z_i\n",
    "$$\n",
    "\n",
    "for the usual Pauli matrices $\\sigma^x, \\sigma^y, \\sigma^z$.\n",
    "\n",
    "A Jordan-Wigner transformation maps the XX Chain to free fermions, which we can diagonalize exactly with a few lines of python codes that are given in [free_fermions_exact.py](https://github.com/tenpy/tenpy_toycodes/blob/main/tenpy_toycodes/free_fermions_exact.py)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "id": "a23c7236",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "E_exact =  -12.053348366664542\n"
     ]
    }
   ],
   "source": [
    "from tenpy_toycodes.free_fermions_exact import XX_model_ground_state_energy\n",
    "\n",
    "print(\"E_exact = \", XX_model_ground_state_energy(L=10, h_staggered=0.))"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "2b8919e4",
   "metadata": {},
   "source": [
    "### Exercise\n",
    "\n",
    "The following code implements the model for the XX Chain hamiltonian, but the MPO lacks some terms. Fill them in!\n",
    "\n",
    "\n",
    "Tip: In Python, `(-1)**i` represents $(-1)^i$.\n",
    "\n",
    "Tip: For the Hamiltonian $$H = \\sum_{i=0}^{N-2} (\\sigma^x_i \\sigma^x_{i+1} + \\sigma^y_i \\sigma^y_{i+1} + \\sigma^z_i \\sigma^z_{i+1}) - h \\sum_{i=0}^{N-1} \\sigma^z_i, $$ a possible MPO matrix W looks like\n",
    "$$ W = \\begin{pmatrix}\n",
    "1 & \\sigma^x & \\sigma^y & \\sigma^z & -h \\sigma^z \\\\\n",
    "0  & 0 &  0 & 0 & \\sigma^x \\\\ \n",
    "0  & 0 &  0 & 0 & \\sigma^y \\\\\n",
    "0  & 0 &  0 & 0 & \\sigma^z \\\\\n",
    "0  & 0 &  0 & 0 & 1 \n",
    "\\end{pmatrix} .$$\n",
    "Which parts do we need here?\n",
    "\n",
    "Compare the energies of DMRG and (imaginary) TEBD to check that you got it correct.\n",
    "\n",
    "**Note** that you have to use the Neel state as initial state to be in the right charge sector:\n",
    "the `|up up up ... up >` state already is an eigenstate of this Hamiltonian, so neither DMRG nor TEBD will modify it!"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "id": "33f562a4",
   "metadata": {},
   "outputs": [],
   "source": [
    "class XXChain:\n",
    "    \"\"\"Simple class generating the Hamiltonian of the \n",
    "    The Hamiltonian reads\n",
    "    .. math ::\n",
    "        H = - J \\\\sum_{i} \\\\sigma^x_i \\\\sigma^x_{i+1} - g \\\\sum_{i} \\\\sigma^z_i\n",
    "    \"\"\"\n",
    "    def __init__(self, L, hs, bc='finite'):\n",
    "        assert bc in ['finite', 'infinite']\n",
    "        self.L, self.d, self.bc = L, 2, bc\n",
    "        self.hs = hs\n",
    "        self.sigmax = np.array([[0., 1.], [1., 0.]])  # Pauli X\n",
    "        self.sigmay = np.array([[0., -1j], [1j, 0.]]) # Pauli Y\n",
    "        self.sigmaz = np.array([[1., 0.], [0., -1.]]) # Pauli Z\n",
    "        self.id = np.eye(2)\n",
    "        self.init_H_bonds()\n",
    "        self.init_H_mpo()\n",
    "\n",
    "    def init_H_bonds(self):\n",
    "        \"\"\"Initialize `H_bonds` hamiltonian.\"\"\"\n",
    "        sx, sy, sz, id = self.sigmax, self.sigmay, self.sigmaz, self.id\n",
    "        d = self.d\n",
    "        nbonds = self.L - 1 if self.bc == 'finite' else self.L\n",
    "        H_list = []\n",
    "        for i in range(nbonds):\n",
    "            hL = hR = 0.5 * self.hs\n",
    "            if self.bc == 'finite':\n",
    "                if i == 0:\n",
    "                    hL = self.hs\n",
    "                if i + 1 == self.L - 1:\n",
    "                    hR = self.hs\n",
    "            H_bond = np.kron(sx, sx) + np.kron(sy, sy)\n",
    "            H_bond = H_bond - hL * (-1)**i * np.kron(sz, id) - hR * (-1)**(i+1) * np.kron(id, sz)\n",
    "            # H_bond has legs ``i, j, i*, j*``\n",
    "            H_list.append(np.reshape(H_bond, [d, d, d, d]))\n",
    "        self.H_bonds = H_list\n",
    "\n",
    "    # (note: not required for TEBD)\n",
    "    def init_H_mpo(self):\n",
    "        \"\"\"Initialize `H_mpo` Hamiltonian.\"\"\"\n",
    "        w_list = []\n",
    "        for i in range(self.L):\n",
    "            w = np.zeros((4, 4, self.d, self.d), dtype=complex)\n",
    "            w[0, 0] = w[3, 3] = self.id\n",
    "            \n",
    "            #raise NotImplementedError(\"add further entries here\")\n",
    "            w[0, 1] = self.sigmax\n",
    "            w[0, 2] = self.sigmay\n",
    "            w[0, 3] = - self.hs * (-1)**i * self.sigmaz\n",
    "            w[1, 3] = self.sigmax\n",
    "            w[2, 3] = self.sigmay\n",
    "            \n",
    "            w_list.append(w)\n",
    "        self.H_mpo = w_list\n",
    "        \n",
    "model = XXChain(9, 4., bc='finite')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "id": "5021c8b7",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "E_exact =  -37.92143925250613\n"
     ]
    }
   ],
   "source": [
    "print(\"E_exact = \", XX_model_ground_state_energy(model.L, model.hs))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "id": "7dd03222",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "dt = 0.10000: E = -37.6207943679329\n",
      "dt = 0.01000: E = -37.8912899426555\n",
      "dt = 0.00100: E = -37.9183076887500\n",
      "dt = 0.00010: E = -37.9209995590774\n",
      "dt = 0.00001: E = -37.9212690303092\n"
     ]
    }
   ],
   "source": [
    "chi_max = 100\n",
    "\n",
    "psi = init_Neel_MPS(model.L, model.d, model.bc)  # important: Neel\n",
    "for dt in [0.1, 0.01, 0.001, 1.e-4, 1.e-5]:\n",
    "    U_bonds = calc_U_bonds(model.H_bonds, dt)\n",
    "    run_TEBD(psi, U_bonds, N_steps=100, chi_max=chi_max, eps=1.e-10)\n",
    "    E = np.sum(psi.bond_expectation_value(model.H_bonds))\n",
    "    print(\"dt = {dt:.5f}: E = {E:.13f}\".format(dt=dt, E=E))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "id": "a4f5fc2e",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "sweep  1: E = -37.9216146988834\n",
      "sweep  2: E = -37.9214392525137\n",
      "sweep  3: E = -37.9214392525061\n",
      "sweep  4: E = -37.9214392525061\n",
      "sweep  5: E = -37.9214392525061\n",
      "sweep  6: E = -37.9214392525061\n",
      "sweep  7: E = -37.9214392525061\n",
      "sweep  8: E = -37.9214392525061\n",
      "sweep  9: E = -37.9214392525061\n",
      "sweep 10: E = -37.9214392525061\n"
     ]
    }
   ],
   "source": [
    "# DMRG again\n",
    "chi_max = 100\n",
    "psi = init_Neel_MPS(model.L, model.d, model.bc)  # important: Neel!\n",
    "eng = SimpleDMRGEngine(psi, model, chi_max=chi_max, eps=1.e-10)\n",
    "for i in range(10):\n",
    "    eng.sweep()\n",
    "    E = np.sum(psi.bond_expectation_value(model.H_bonds))\n",
    "    #print(psi.get_chi())\n",
    "    print(\"sweep {i:2d}: E = {E:.13f}\".format(i=i + 1, E=E))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "42fe4054",
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "markdown",
   "id": "4969359f",
   "metadata": {},
   "source": [
    "## Time evolution of the Neel state under the XX chain\n",
    "\n",
    "We will now consider the Neel state as an initial state for (real-)time evolution, i.e., calculate\n",
    "$$ \\vert \\psi(t)\\rangle =e^{-i H t} \\vert\\uparrow \\downarrow \\uparrow \\downarrow \\dots\\rangle$$\n",
    "under the Hamiltonian of the XX chain (with staggered field).\n",
    "\n",
    "Again, we can use the mapping to free fermions to calculate some quantities exactly.\n",
    "We will focus on the half chain entanglement entropy.\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 28,
   "id": "9d9fc268",
   "metadata": {},
   "outputs": [],
   "source": [
    "from tenpy_toycodes.free_fermions_exact import XX_model_time_evolved_entropies\n",
    "\n",
    "dt = 0.1\n",
    "tmax = 4.\n",
    "L = 50\n",
    "hs = 0.\n",
    "model = XXChain(L, hs)\n",
    "\n",
    "times_exact = np.arange(0., tmax, dt)\n",
    "S_exact = XX_model_time_evolved_entropies(L=L, h_staggered=hs, time_list=times_exact)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "777211cf",
   "metadata": {},
   "source": [
    "Running TEBD works like this:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 29,
   "id": "12f349e4",
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "t=0.00\n",
      "t=0.10\n",
      "t=0.20\n",
      "t=0.30\n",
      "t=0.40\n",
      "t=0.50\n",
      "t=0.60\n",
      "t=0.70\n",
      "t=0.80\n",
      "t=0.90\n",
      "t=1.00\n",
      "t=1.10\n",
      "t=1.20\n",
      "t=1.30\n",
      "t=1.40\n",
      "t=1.50\n",
      "t=1.60\n",
      "t=1.70\n",
      "t=1.80\n",
      "t=1.90\n",
      "t=2.00\n",
      "t=2.10\n",
      "t=2.20\n",
      "t=2.30\n",
      "t=2.40\n",
      "t=2.50\n",
      "t=2.60\n",
      "t=2.70\n",
      "t=2.80\n",
      "t=2.90\n",
      "t=3.00\n",
      "t=3.10\n",
      "t=3.20\n",
      "t=3.30\n",
      "t=3.40\n",
      "t=3.50\n",
      "t=3.60\n",
      "t=3.70\n",
      "t=3.80\n",
      "t=3.90\n"
     ]
    }
   ],
   "source": [
    "chi_max = 30\n",
    "\n",
    "psi = init_Neel_MPS(L, 2, bc='finite')\n",
    "U_bonds = calc_U_bonds(model.H_bonds, 1.j * dt) # here, imaginary dt = real time evolution\n",
    "t = 0.\n",
    "times_tebd = []\n",
    "S_tebd = []\n",
    "while t < tmax: \n",
    "    times_tebd.append(t)\n",
    "    S_tebd.append(psi.entanglement_entropy()[(L-1)//2])\n",
    "    print(f\"t={t:.2f}\")\n",
    "    t += dt\n",
    "    run_TEBD(psi, U_bonds, N_steps=1, chi_max=chi_max, eps=1.e-7)\n"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "d5db1896-bca5-483f-aa96-60c6db4aeb30",
   "metadata": {},
   "source": [
    "For reference, one can also run TDVP with the [e_tdvp.py](https://github.com/tenpy/tenpy_toycodes/blob/main/tenpy_toycodes/e_tdvp.py) in a very similar pattern as follows.\n",
    "If you know how TDVP works, try to take a look and spot the structure in the code.\n",
    "Otherwise, you can also consider it a black box for now.\n",
    "\n",
    "The toycode implements the TDVP time evolution for finite MPS with the `SimpleTDVPEngine`.\n",
    "It implements both the true TDVP with one-site updates in `sweep_one_site`, and `sweep_two_site` that allows to grow the bond dimension.\n",
    "\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 30,
   "id": "7814c1e9",
   "metadata": {},
   "outputs": [],
   "source": [
    "from tenpy_toycodes.e_tdvp import SimpleTDVPEngine"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 31,
   "id": "9c6f5f2e",
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "t=0.00, chi_max = 1\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/home/johannes/postdoc/tenpy_other/tenpy_toycodes/tenpy_toycodes/e_tdvp.py:242: UserWarning: Trace of LinearOperator not available, it will be estimated. Provide `traceA` to ensure performance.\n",
      "  return expm_multiply((-1.j*dt) * H, psi0)\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "t=0.10, chi_max = 4\n",
      "t=0.20, chi_max = 10\n",
      "t=0.30, chi_max = 12\n",
      "t=0.40, chi_max = 18\n",
      "t=0.50, chi_max = 23\n",
      "t=0.60, chi_max = 28\n",
      "t=0.70, chi_max = 30\n",
      "t=0.80, chi_max = 30\n",
      "t=0.90, chi_max = 30\n",
      "t=1.00, chi_max = 30\n",
      "t=1.10, chi_max = 30\n",
      "t=1.20, chi_max = 30\n",
      "t=1.30, chi_max = 30\n",
      "t=1.40, chi_max = 30\n",
      "t=1.50, chi_max = 30\n",
      "t=1.60, chi_max = 30\n",
      "t=1.70, chi_max = 30\n",
      "t=1.80, chi_max = 30\n",
      "t=1.90, chi_max = 30\n",
      "t=2.00, chi_max = 30\n",
      "t=2.10, chi_max = 30\n",
      "t=2.20, chi_max = 30\n",
      "t=2.30, chi_max = 30\n",
      "t=2.40, chi_max = 30\n",
      "t=2.50, chi_max = 30\n",
      "t=2.60, chi_max = 30\n",
      "t=2.70, chi_max = 30\n",
      "t=2.80, chi_max = 30\n",
      "t=2.90, chi_max = 30\n",
      "t=3.00, chi_max = 30\n",
      "t=3.10, chi_max = 30\n",
      "t=3.20, chi_max = 30\n",
      "t=3.30, chi_max = 30\n",
      "t=3.40, chi_max = 30\n",
      "t=3.50, chi_max = 30\n",
      "t=3.60, chi_max = 30\n",
      "t=3.70, chi_max = 30\n",
      "t=3.80, chi_max = 30\n",
      "t=3.90, chi_max = 30\n"
     ]
    }
   ],
   "source": [
    "chi_max = 30\n",
    "t_switch = 1.\n",
    "\n",
    "psi = init_Neel_MPS(L, 2, bc='finite')\n",
    "eng = SimpleTDVPEngine(psi, model, chi_max=chi_max, eps=1.e-7)\n",
    "\n",
    "t = 0.\n",
    "times_tdvp = []\n",
    "S_tdvp = []\n",
    "while t < tmax: \n",
    "    times_tdvp.append(t)\n",
    "    S_tdvp.append(psi.entanglement_entropy()[(L-1)//2])\n",
    "    print(f\"t={t:.2f}, chi_max = {max(psi.get_chi()):d}\")\n",
    "    t += dt\n",
    "    if t < t_switch:\n",
    "        eng.sweep_two_site(dt)\n",
    "    else:\n",
    "        eng.sweep_one_site(dt)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "8139c6a8",
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": 32,
   "id": "667f930e",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.legend.Legend at 0x7f95effc5c60>"
      ]
     },
     "execution_count": 32,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 960x720 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.plot(times_exact, S_exact, label=\"exact\")\n",
    "plt.plot(times_tebd, S_tebd, label=\"TEBD\")\n",
    "plt.plot(times_tdvp, S_tdvp, label=\"TDVP\")\n",
    "\n",
    "plt.xlabel('time $t$')\n",
    "plt.ylabel('half-chain entropy $S$')\n",
    "plt.legend(loc='best')"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "a83ffdd6",
   "metadata": {},
   "source": [
    "### Exercise\n",
    "\n",
    "Read the code of `e_tdvp.py` and try to see the general structure of how it works."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "9553b647",
   "metadata": {},
   "source": [
    "### Exercise\n",
    "\n",
    "Add curves for smaller (or larger) chi to the plot above. (It might take a little while to run for large chi...).\n",
    "\n",
    "Try switching earlier or later from two-site to one-site TDVP.\n",
    "\n",
    "What happens if you switch on the staggered field?\n",
    "\n",
    "\n",
    "**NOTE**: You can avoid having to rerun the time evolution if you make copies of the results `S_tdvp` and similar lists.\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 33,
   "id": "ad4d0c74",
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "t=0.00, chi_max = 1\n",
      "t=0.10, chi_max = 4\n",
      "t=0.20, chi_max = 10\n",
      "t=0.30, chi_max = 10\n",
      "t=0.40, chi_max = 10\n",
      "t=0.50, chi_max = 10\n",
      "t=0.60, chi_max = 10\n",
      "t=0.70, chi_max = 10\n",
      "t=0.80, chi_max = 10\n",
      "t=0.90, chi_max = 10\n",
      "t=1.00, chi_max = 10\n",
      "t=1.10, chi_max = 10\n",
      "t=1.20, chi_max = 10\n",
      "t=1.30, chi_max = 10\n",
      "t=1.40, chi_max = 10\n",
      "t=1.50, chi_max = 10\n",
      "t=1.60, chi_max = 10\n",
      "t=1.70, chi_max = 10\n",
      "t=1.80, chi_max = 10\n",
      "t=1.90, chi_max = 10\n",
      "t=2.00, chi_max = 10\n",
      "t=2.10, chi_max = 10\n",
      "t=2.20, chi_max = 10\n",
      "t=2.30, chi_max = 10\n",
      "t=2.40, chi_max = 10\n",
      "t=2.50, chi_max = 10\n",
      "t=2.60, chi_max = 10\n",
      "t=2.70, chi_max = 10\n",
      "t=2.80, chi_max = 10\n",
      "t=2.90, chi_max = 10\n",
      "t=3.00, chi_max = 10\n",
      "t=3.10, chi_max = 10\n",
      "t=3.20, chi_max = 10\n",
      "t=3.30, chi_max = 10\n",
      "t=3.40, chi_max = 10\n",
      "t=3.50, chi_max = 10\n",
      "t=3.60, chi_max = 10\n",
      "t=3.70, chi_max = 10\n",
      "t=3.80, chi_max = 10\n",
      "t=3.90, chi_max = 10\n"
     ]
    }
   ],
   "source": [
    "chi_max = 10\n",
    "\n",
    "psi = init_Neel_MPS(L, 2, bc='finite')\n",
    "eng = SimpleTDVPEngine(psi, model, chi_max=chi_max, eps=1.e-7)\n",
    "\n",
    "t = 0.\n",
    "times_tdvp_chi_10 = []\n",
    "S_tdvp_chi_10 = []\n",
    "while t < tmax: \n",
    "    times_tdvp_chi_10.append(t)\n",
    "    S_tdvp_chi_10.append(psi.entanglement_entropy()[(L-1)//2])\n",
    "    print(f\"t={t:.2f}, chi_max = {max(psi.get_chi()):d}\")\n",
    "    t += dt\n",
    "    if t < t_switch:\n",
    "        eng.sweep_two_site(dt)\n",
    "    else:\n",
    "        eng.sweep_one_site(dt)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 34,
   "id": "f0989680",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.legend.Legend at 0x7f95effc4b50>"
      ]
     },
     "execution_count": 34,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 960x720 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.plot(times_exact, S_exact, label=\"exact\")\n",
    "plt.plot(times_tebd, S_tebd, label=r\"TEBD, $\\chi=30$\")\n",
    "plt.plot(times_tdvp, S_tdvp, label=r\"TDVP, $\\chi=30$\")\n",
    "plt.plot(times_tdvp_chi_10, S_tdvp_chi_10, label=r\"TDVP, $\\chi=10$\")\n",
    "\n",
    "\n",
    "plt.xlabel('time $t$')\n",
    "plt.ylabel('half-chain entropy $S$')\n",
    "plt.legend(loc='best')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "d16df3aa",
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "markdown",
   "id": "1e99ab49",
   "metadata": {},
   "source": [
    "### Advanced exercises - if you're an expert and have time left ;-)\n",
    "\n",
    "\n",
    "- Obtain the ground state of the transverse field ising model at the critical point with DMRG.\n",
    "  Try to plot the corrlation function as a function of `j-i`.\n",
    "  What form does it have? Is an MPS a good ansatz for that?\n",
    "- Calling `SimpleMPS.correlation_function` in a loop over `j` for fixed `i` is inefficient for large `j-i`. \n",
    "  Try to rewrite the correlation function to obtain the values for all `j>i` up to some cutoff in a single loop.\n",
    "- Look at the light-cone after a local quench of the XX chain, similarly as is done in  `e_tdvp.example_TDVP_tf_ising_lightcone`. \n",
    "  How does the speed of the light cone change with the staggered field?"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "1dfbc061",
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "b9d25343",
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "da649492-fe07-437f-931a-7843a3e4a6a4",
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "97801804-24e0-4261-912f-699fc8b93228",
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
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   "language": "python",
   "name": "python3"
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  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
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   "file_extension": ".py",
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