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 cell 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 `*.py` python files from \n",
    "\n",
    "https://github.com/jhauschild/WinterschoolBarcelona2021\n",
    "\n",
    "in the same folder as your notebook."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "id": "8d42e939",
   "metadata": {},
   "outputs": [],
   "source": [
    "#!pip install git+git://github.com/jhauschild/WinterschoolBarcelona2021\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/jhauschild/WinterschoolBarcelona2021/blob/main/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 toycodes.a_mps import init_FM_MPS, init_Neel_MPS"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "id": "a4f0ecc0",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "<toycodes.a_mps.SimpleMPS object at 0x7f3016846370>\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": "markdown",
   "id": "0966eb59",
   "metadata": {},
   "source": [
    "# toy codes: b_model.py\n",
    "\n",
    "The file [b_model.py](https://github.com/jhauschild/WinterschoolBarcelona2021/blob/main/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": 7,
   "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 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": 8,
   "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/jhauschild/WinterschoolBarcelona2021/blob/main/toycodes/c_tebd.py) implements the TEBD algorithm, that we already learned about yesterday. \n",
    "\n",
    "\n",
    "**You don't have to read the code now; we will only use it for comparison with the other algorithms**.\n",
    "\n",
    "\n",
    "You can run TEBD with imaginary time evolutinon to find the ground state like this:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "id": "d6c0d701",
   "metadata": {},
   "outputs": [],
   "source": [
    "from toycodes.c_tebd import calc_U_bonds, run_TEBD"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "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": "bb7b318b",
   "metadata": {},
   "source": [
    "# toy codes: d_dmrg.py\n",
    "\n",
    "The file [d_dmrg.py](https://github.com/jhauschild/WinterschoolBarcelona2021/blob/main/toycodes/d_dmrg.py) implements the DMRG algorithm.\n",
    "It can be called like this:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "id": "3196f562",
   "metadata": {},
   "outputs": [],
   "source": [
    "from toycodes.d_dmrg import SimpleDMRGEngine, SimpleHeff2"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "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/jhauschild/WinterschoolBarcelona2021/blob/main/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": 13,
   "id": "b4e7e445",
   "metadata": {},
   "outputs": [],
   "source": [
    "model = TFIModel(L=20, J=1., g=1.0, bc='finite')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "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": 15,
   "id": "76ab2cc8",
   "metadata": {},
   "outputs": [],
   "source": [
    "model = TFIModel(L=2, J=1., g=0.2, bc='infinite')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "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 = -1.0100254885274\n",
      "sweep  4: E/L = -1.0100252544815\n",
      "sweep  5: E/L = -1.0966989374098\n",
      "sweep  6: E/L = -3.9544957910380\n",
      "sweep  7: E/L = -1.0100252541230\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": 17,
   "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": 18,
   "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 =7\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": 19,
   "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 =7\n",
      "runnning DMRG for L=2, g=0.30, bc=infinite, chi_max=50\n",
      "max chi =12\n",
      "runnning DMRG for L=2, g=0.40, bc=infinite, chi_max=50\n",
      "max chi =15\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": 20,
   "id": "4ce49bc6",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.legend.Legend at 0x7f3014ed2f70>"
      ]
     },
     "execution_count": 20,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 900x600 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "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 $\\sigma^z$, $\\sigma^x$.\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/jhauschild/WinterschoolBarcelona2021/blob/main/toycodes/free_fermions_exact.py)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "id": "a23c7236",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "E_exact =  -12.053348366664542\n"
     ]
    }
   ],
   "source": [
    "from 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",
    "\n",
    "Compare the energies of DMRG and (imaginary) TEBD to check that you got it correct.\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": 22,
   "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": 23,
   "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": 24,
   "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": 25,
   "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 and compare it to TEBD:\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "id": "9d9fc268",
   "metadata": {},
   "outputs": [],
   "source": [
    "from 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": [
    "For reference, will will also compare to a TEBD run:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "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": "8e3a0072",
   "metadata": {},
   "source": [
    "# toy code: e_tdvp.py\n",
    "\n",
    "The file [e_tdvp.py](https://github.com/jhauschild/WinterschoolBarcelona2021/blob/main/toycodes/e_tdvp.py) 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": 28,
   "id": "7814c1e9",
   "metadata": {},
   "outputs": [],
   "source": [
    "from toycodes.e_tdvp import SimpleTDVPEngine"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 29,
   "id": "9c6f5f2e",
   "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 = 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": 30,
   "id": "667f930e",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.legend.Legend at 0x7f3014dc3fd0>"
      ]
     },
     "execution_count": 30,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 900x600 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "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": 31,
   "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": 32,
   "id": "f0989680",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.legend.Legend at 0x7f3014cc8a30>"
      ]
     },
     "execution_count": 32,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 900x600 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "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",
    "- 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": []
  }
 ],
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  "kernelspec": {
   "display_name": "Python 3",
   "language": "python",
   "name": "python3"
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  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
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   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
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