solution_3_dmrg.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "id": "2fe29049",
   "metadata": {},
   "source": [
    "# Solutions to DMRG runs\n",
    "\n",
    "In this notebook, we use the `SimpleDMRGEngine` class from `tenpy_toycodes/d_dmrg.py` to run DMRG and find MPS ground states."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "id": "56956a97",
   "metadata": {},
   "outputs": [],
   "source": [
    "# standard imports and cosmetics\n",
    "\n",
    "import numpy as np\n",
    "\n",
    "import matplotlib.pyplot as plt\n",
    "\n",
    "np.set_printoptions(precision=5, suppress=True, linewidth=100, threshold=50)\n",
    "plt.rcParams['figure.dpi'] = 150"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "238d735d-7666-4181-bf50-481d8cc61adb",
   "metadata": {},
   "source": [
    "In previous notebooks, we learned how to initialize `SimpleMPS`..."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "id": "8b2cfaee",
   "metadata": {},
   "outputs": [],
   "source": [
    "from tenpy_toycodes.a_mps import SimpleMPS, init_FM_MPS, init_Neel_MPS"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "id": "fd3a1a46-378d-4041-86ec-4ae992de0a7e",
   "metadata": {},
   "outputs": [],
   "source": [
    "L = 12"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "id": "a4f0ecc0",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "<tenpy_toycodes.a_mps.SimpleMPS object at 0x7f377d99a650>\n",
      "[1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1.]\n"
     ]
    }
   ],
   "source": [
    "psi_FM = init_FM_MPS(L=L, d=2, bc='finite')\n",
    "print(psi_FM)\n",
    "SigmaZ = np.diag([1., -1.])\n",
    "print(psi_FM.site_expectation_value(SigmaZ))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "id": "fe6d3e07-f52d-466e-913d-245e541a0ced",
   "metadata": {},
   "outputs": [],
   "source": [
    "def init_PM_MPS(L, bc='finite'):\n",
    "    \"\"\"Return a paramagnetic MPS (= product state with all spins pointing in +x direction)\"\"\"\n",
    "    d = 2\n",
    "    B = np.zeros([1, d, 1], dtype=float)\n",
    "    B[0, 0, 0] = 1./np.sqrt(2)\n",
    "    B[0, 1, 0] = 1./np.sqrt(2)\n",
    "    S = np.ones([1], dtype=float)\n",
    "    Bs = [B.copy() for i in range(L)]\n",
    "    Ss = [S.copy() for i in range(L)]\n",
    "    return SimpleMPS(Bs, Ss, bc=bc)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "bcb5c97c-5f8b-4c1c-94c6-d3c2041db75c",
   "metadata": {},
   "source": [
    "... and how to initialize the `TFIModel`."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "id": "d439f112",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "<H_bonds> =  [-1. -1. -1. -1. -1. -1. -1. -1. -1. -1. -1.]\n",
      "energy: -11.0\n"
     ]
    }
   ],
   "source": [
    "from tenpy_toycodes.b_model import TFIModel\n",
    "\n",
    "g = 1.2\n",
    "model = TFIModel(L=L, J=1., g=g, 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": "93368432-f304-4327-987c-b9c12a818c26",
   "metadata": {},
   "source": [
    "\n",
    "For small enough system size $L \\lesssim 16$, you can compare the energies to exact diagonalization in the full Hilbert space (which is exponentially expensive!):"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "id": "25871fc0-6b4f-4266-b78c-c25519210372",
   "metadata": {},
   "outputs": [],
   "source": [
    "from tenpy_toycodes.tfi_exact import finite_gs_energy\n",
    "\n",
    "if L <= 16:\n",
    "    energy_exact = finite_gs_energy(L=L, J=1., g=g)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "69be6188-dfad-4313-90dc-ca0be87793ad",
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "markdown",
   "id": "bb7b318b",
   "metadata": {},
   "source": [
    "## The DMRG algorithm\n",
    "\n",
    "The file `tenpy_toycodes/d_dmrg.py` implements the DMRG algorithm.\n",
    "It can be called like this:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "id": "3196f562",
   "metadata": {},
   "outputs": [],
   "source": [
    "from tenpy_toycodes.d_dmrg import SimpleDMRGEngine, SimpleHeff2"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "id": "ffc67843",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "sweep  1: E = -16.7887686421687\n",
      "sweep  2: E = -16.7865402682303\n",
      "sweep  3: E = -16.7865402285887\n",
      "sweep  4: E = -16.7865402285887\n",
      "sweep  5: E = -16.7865402285887\n",
      "sweep  6: E = -16.7865402285887\n",
      "sweep  7: E = -16.7865402285887\n",
      "sweep  8: E = -16.7865402285887\n",
      "sweep  9: E = -16.7865402285887\n",
      "sweep 10: E = -16.7865402285887\n",
      "final bond dimensions:  [2, 4, 8, 14, 15, 15, 15, 14, 8, 4, 2]\n",
      "magnetization in X = 0.81887\n",
      "magnetization in Z = 0.00000\n",
      "err in energy = 0.000e+00\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))\n",
    "if model.L <= 16:\n",
    "    E_exact = finite_gs_energy(L=model.L, J=model.J, g=model.g)\n",
    "    print(\"err in energy = {err:.3e}\".format(err=E - E_exact))"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "b0eee6bf",
   "metadata": {},
   "source": [
    "### Exercise: read d_dmrg.py\n",
    "\n",
    "Read the code of `tenpy_toycodes/d_dmrg.py` and try to undertstand the general structure of how it works.\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "97226a24-892e-493a-88f4-9394615f240a",
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "markdown",
   "id": "2a57a415-a81d-46f1-8366-533466ff70ee",
   "metadata": {},
   "source": [
    "### Exercise: measure correlation functions\n",
    "\n",
    "Just looking at expectation values of local operators is not enough.\n",
    "Also measure correlation functions $\\langle Z_{L/4} Z_{3L/4} \\rangle$."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "id": "8fc2a15b-f45d-4073-aa56-7af10cb01bdc",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "correlation <Sz_L/4 Sz_3L/4> = 0.08762\n"
     ]
    }
   ],
   "source": [
    "corr = psi.correlation_function(model.sigmaz, model.L//4, model.sigmaz, model.L * 3 // 4)\n",
    "print(\"correlation <Sz_L/4 Sz_3L/4> = {corr:.5f}\".format(corr=corr))\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "76d1d8ed-c18d-4a84-8faf-f5390cd7e0b4",
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "markdown",
   "id": "4799e6ed-f16d-4189-b224-8d1e972bf14d",
   "metadata": {},
   "source": [
    "### Exercise: DMRG runs\n",
    "\n",
    "Try running DMRG for various different parameters:\n",
    "\n",
    "- Change the bond dimension `chi` and truncation threashold `eps`.\n",
    "- Change the system size `L`\n",
    "- Change the model parameter `g` (at fixed $J=1$) to both the ferromagnetic phase $g<J$ \n",
    "  and the paramagnetic phase $g>1$.\n",
    "- Change the initial state.\n",
    "\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "id": "c489cca3-3b21-4602-8329-6fb9e06137ff",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "sweep  1: E = -16.7887686421687\n",
      "sweep  2: E = -16.7865402682303\n",
      "sweep  3: E = -16.7865402285887\n",
      "sweep  4: E = -16.7865402285887\n",
      "sweep  5: E = -16.7865402285887\n",
      "sweep  6: E = -16.7865402285887\n",
      "sweep  7: E = -16.7865402285887\n",
      "sweep  8: E = -16.7865402285887\n",
      "sweep  9: E = -16.7865402285887\n",
      "sweep 10: E = -16.7865402285887\n",
      "final bond dimensions:  [2, 4, 8, 14, 15, 15, 15, 14, 8, 4, 2]\n",
      "magnetization in X = 0.81887\n",
      "magnetization in Z = 0.00000\n",
      "err in energy = -6.040e-14\n",
      "correlation <Sz_L/4 Sz_3L/4> = 0.08762\n"
     ]
    }
   ],
   "source": [
    "chi_max, eps = 15, 1.e-10\n",
    "g = 1.2\n",
    "L = 12\n",
    "\n",
    "model = TFIModel(L=L, J=1., g=g, bc='finite')\n",
    "psi = init_FM_MPS(model.L, model.d, model.bc)\n",
    "eng = SimpleDMRGEngine(psi, model, chi_max=chi_max, eps=eps)\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))\n",
    "if model.L <= 16:\n",
    "    E_exact = finite_gs_energy(L=model.L, J=model.J, g=model.g)\n",
    "    print(\"err in energy = {err:.3e}\".format(err=E - E_exact))\n",
    "corr = psi.correlation_function(model.sigmaz, model.L//4, model.sigmaz, model.L * 3 // 4)\n",
    "print(\"correlation <Sz_L/4 Sz_3L/4> = {corr:.5f}\".format(corr=corr))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "d8ff6307-aad9-4cb4-99ba-a3e75873d273",
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "markdown",
   "id": "efe930da-18c3-4091-8ea9-412b562c7857",
   "metadata": {},
   "source": [
    "### Exercise: Phase diagram\n",
    "\n",
    "To map out the phase diagram, it can be convenient to define a function that just runs DMRG for a given model. Fill in the below template. Use it obtain and plot the energy, correlations and magnetizations for different $L$ against $g$."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "id": "8157051c-7bfa-407b-a889-536e821eedf6",
   "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",
    "    psi = init_FM_MPS(model.L, model.d, model.bc)\n",
    "    eng = SimpleDMRGEngine(psi, model, chi_max=chi_max, eps=eps)\n",
    "    for i in range(10):\n",
    "        E_dmrg = eng.sweep() \n",
    "    return psi"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "id": "5a7682dc-483f-4ada-8bcf-b4f9443c256e",
   "metadata": {},
   "outputs": [],
   "source": [
    "results_all = {}\n",
    "# TIP: comment this out after the first run to avoid overriding your data!"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "id": "c1d120e7-0ecc-4800-857b-f12cd3fd23e7",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "runnning DMRG for L=64, g=0.10, bc=finite, chi_max=50\n",
      "runnning DMRG for L=64, g=0.50, bc=finite, chi_max=50\n",
      "runnning DMRG for L=64, g=0.80, bc=finite, chi_max=50\n",
      "runnning DMRG for L=64, g=0.90, bc=finite, chi_max=50\n",
      "runnning DMRG for L=64, g=1.00, bc=finite, chi_max=50\n",
      "runnning DMRG for L=64, g=1.10, bc=finite, chi_max=50\n",
      "runnning DMRG for L=64, g=1.20, bc=finite, chi_max=50\n",
      "runnning DMRG for L=64, g=1.50, bc=finite, chi_max=50\n"
     ]
    }
   ],
   "source": [
    "L = 64  # rerun for different L!\n",
    "\n",
    "mag_X = []\n",
    "mag_Z = []\n",
    "E = []\n",
    "corr = []\n",
    "max_chi = []\n",
    "\n",
    "gs = [0.1, 0.5, 0.8, 0.9, 1.0, 1.1, 1.2, 1.5]\n",
    "for g in gs:\n",
    "    model = TFIModel(L=L, J=1., g=g, bc='finite')\n",
    "    psi = run_DMRG(model)\n",
    "    mag_X.append(np.mean(psi.site_expectation_value(model.sigmax)))\n",
    "    mag_Z.append(np.mean(psi.site_expectation_value(model.sigmaz)))\n",
    "    E.append(np.sum(psi.bond_expectation_value(model.H_bonds)))\n",
    "    corr.append(psi.correlation_function(model.sigmaz, model.L//4, model.sigmaz, model.L * 3 // 4))\n",
    "    max_chi.append(max(psi.get_chi()))\n",
    "\n",
    "results_all[L] = {\n",
    "    'g': gs,\n",
    "    'mag_X': mag_X,\n",
    "    'mag_Z': mag_Z,\n",
    "    'E': E,\n",
    "    'corr': corr,\n",
    "    'max_chi': max_chi\n",
    "}"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "id": "bdc10397-269f-469d-a2c0-1bb0232dfbb0",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.legend.Legend at 0x7f377c808dc0>"
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     },
     "execution_count": 15,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
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\n",
      "text/plain": [
       "<Figure size 960x720 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "key = 'corr'\n",
    "\n",
    "plt.figure()\n",
    "for L in results_all:\n",
    "    res_L = results_all[L]\n",
    "    plt.plot(res_L['g'], res_L[key], marker='o', label=\"L={L:d}\".format(L=L))\n",
    "plt.xlabel('g')\n",
    "plt.ylabel(key)\n",
    "plt.legend(loc='best')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "id": "2065491b-7972-4034-9fee-8fe67e6546b5",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.legend.Legend at 0x7f3774685510>"
      ]
     },
     "execution_count": 16,
     "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": [
    "key = 'mag_X'\n",
    "\n",
    "plt.figure()\n",
    "for L in results_all:\n",
    "    res_L = results_all[L]\n",
    "    plt.plot(res_L['g'], res_L[key], marker='o', label=\"L={L:d}\".format(L=L))\n",
    "plt.xlabel('g')\n",
    "plt.ylabel(key)\n",
    "plt.legend(loc='best')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "id": "3ff5c7e8-8090-4fec-a723-7f04968dfcd5",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.legend.Legend at 0x7f37742dd120>"
      ]
     },
     "execution_count": 17,
     "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": [
    "key = 'mag_Z'\n",
    "\n",
    "plt.figure()\n",
    "for L in results_all:\n",
    "    res_L = results_all[L]\n",
    "    plt.plot(res_L['g'], res_L[key], marker='o', label=\"L={L:d}\".format(L=L))\n",
    "plt.xlabel('g')\n",
    "plt.ylabel(key)\n",
    "plt.legend(loc='best')"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "6b3a0150-5816-458a-b5f7-942426ffc6da",
   "metadata": {},
   "source": [
    "You might wonder what is going on in the plot of `mag_Z` above in the ferromagnetic phase `g < J`.\n",
    "In this phase, the system spontaneoulsy breaks the symmetry in the thermodynamic limit, with two ground states  $ \\lvert Z \\approx \\pm 1\\rangle$. In the finite systems, there is a small splitting into the symmetric and anti-symmetric superpositions $\\lvert Z \\approx 1 \\rangle \\pm \\lvert Z \\approx -1 \\rangle $ (\"cat states\"), so that the true finite-L ground state has $\\langle Z\\rangle = 0$.\n",
    "However, for larger $L$, this splitting can no longer be resolved, and DMRG breaks the symmetry since this lowers energy due to a smaller truncation error - a cat state needs significantly larger bond dimensions at the same precision."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "id": "fec23ec9-e521-4fcb-94a9-d696cdd98c9a",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.legend.Legend at 0x7f37743555d0>"
      ]
     },
     "execution_count": 18,
     "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": [
    "key = 'max_chi'\n",
    "\n",
    "plt.figure()\n",
    "for L in results_all:\n",
    "    res_L = results_all[L]\n",
    "    plt.plot(res_L['g'], res_L[key], marker='o', label=\"L={L:d}\".format(L=L))\n",
    "plt.xlabel('g')\n",
    "plt.ylabel(key)\n",
    "plt.legend(loc='best')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "6d59b6c5-551f-4b2a-b7cd-7d8c1581de67",
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "markdown",
   "id": "ffdc381f-f5a7-42fe-85b9-ce43e51a7133",
   "metadata": {},
   "source": [
    "## Infinite DMRG"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "afbf96cc-b723-4826-a0be-9f7de039a659",
   "metadata": {},
   "source": [
    "The given DMRG code also works with `bc='infinite'` boundary conditions of the model and state.\n",
    "The given `SimpleDMRG` code also allows to run infinite DMRG, simply by replacing the `bc='finite'` for both the model and the MPS. \n",
    "\n",
    "- Look at the implementation of `d_dmrg.py` (and `a_mps.py`) to see where the differences are.\n",
    "\n",
    "Again, we can compare to analytic calculations possible for the Transverse Field Ising model.\n",
    "  "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "id": "98e49bcb-9dc9-4dc1-aff3-f8d08fff5085",
   "metadata": {},
   "outputs": [],
   "source": [
    "from tenpy_toycodes.tfi_exact import infinite_gs_energy"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "cd9364b6-7885-4a65-a695-000cb8720f9d",
   "metadata": {},
   "source": [
    "\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",
    "Note that we now use the `mean` to calculate densities of observables instead of extensive quantities:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "id": "545b6a75-1550-433e-8763-968281137a41",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "sweep  1: E/L = -1.1691320258028\n",
      "sweep  2: E/L = -1.1859218684668\n",
      "sweep  3: E/L = -1.1830439651388\n",
      "sweep  4: E/L = -1.1768668631138\n",
      "sweep  5: E/L = -1.1725334866568\n",
      "sweep  6: E/L = -1.1700487255459\n",
      "sweep  7: E/L = -1.1688086884548\n",
      "sweep  8: E/L = -1.1682394025940\n",
      "sweep  9: E/L = -1.1679905285657\n",
      "sweep 10: E/L = -1.1678847922595\n",
      "final bond dimensions:  [10, 10]\n",
      "magnetization density in X = 0.44415\n",
      "magnetization density in Z = -0.00000\n",
      "err in energy = -7.528e-05\n"
     ]
    }
   ],
   "source": [
    "model = TFIModel(L=2, J=1., g=0.8, bc='infinite')  # just change bc='infinite' here\n",
    "\n",
    "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 density in X = {mag_x:.5f}\".format(mag_x=mag_x))\n",
    "print(\"magnetization density in Z = {mag_z:.5f}\".format(mag_z=mag_z))\n",
    "E_exact = infinite_gs_energy(model.J, model.g)\n",
    "print(\"err in energy = {err:.3e}\".format(err=E - E_exact))"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "0aee66eb-d748-4b24-8618-1c30209273ab",
   "metadata": {},
   "source": [
    "### Exercise: Infinite DMRG\n",
    "\n",
    "Try running the infinite DMRG code. How many sweeps do you now need to perform to converge now?\n",
    "  Does it depend on `g` and `chi`?"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "id": "ba06417d-f47d-4e97-a89e-1138b5803826",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "sweep 10: E/L = -1.1678847922595\n",
      "sweep 20: E/L = -1.1678095166355\n",
      "sweep 30: E/L = -1.1678581030541\n",
      "sweep 40: E/L = -1.1678095085625\n",
      "sweep 50: E/L = -1.1678095085207\n",
      "sweep 60: E/L = -1.1678095085207\n",
      "sweep 70: E/L = -1.1678095085207\n",
      "sweep 80: E/L = -1.1678095085207\n",
      "sweep 90: E/L = -1.1678095085207\n",
      "sweep 100: E/L = -1.1678095085207\n",
      "final bond dimensions:  [10, 10]\n",
      "magnetization density in X = 0.44407\n",
      "magnetization density in Z = 0.88011\n",
      "err in energy = -6.994e-14\n"
     ]
    }
   ],
   "source": [
    "model = TFIModel(L=2, J=1., g=0.8, bc='infinite')  # just change bc='infinite' here\n",
    "\n",
    "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(100):\n",
    "    E_dmrg = eng.sweep()\n",
    "    E = np.mean(psi.bond_expectation_value(model.H_bonds))\n",
    "    if i % 10 == 9:\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 density in X = {mag_x:.5f}\".format(mag_x=mag_x))\n",
    "print(\"magnetization density in Z = {mag_z:.5f}\".format(mag_z=mag_z))\n",
    "E_exact = infinite_gs_energy(model.J, model.g)\n",
    "print(\"err in energy = {err:.3e}\".format(err=E - E_exact))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "a1f1b13c-fa6b-4f39-8fa6-15af3b835846",
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "id": "4aa273e3-d05d-45d7-9b14-0d52610d3f71",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "sweep 10: E/L = -1.2734731285873\n",
      "sweep 20: E/L = -1.2732892142506\n",
      "sweep 30: E/L = -1.2732583617401\n",
      "sweep 40: E/L = -1.2732481551659\n",
      "sweep 50: E/L = -1.2732435768774\n",
      "sweep 60: E/L = -1.2732411321859\n",
      "sweep 70: E/L = -1.2732396732724\n",
      "sweep 80: E/L = -1.2732387344249\n",
      "sweep 90: E/L = -1.2732380971634\n",
      "sweep 100: E/L = -1.2732376474834\n",
      "final bond dimensions:  [10, 10]\n",
      "magnetization density in X = 0.63816\n",
      "magnetization density in Z = 0.00000\n",
      "err in energy = 1.897e-06\n"
     ]
    }
   ],
   "source": [
    "model = TFIModel(L=2, J=1., g=1.0, bc='infinite')  # just change bc='infinite' here\n",
    "\n",
    "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(100):\n",
    "    E_dmrg = eng.sweep()\n",
    "    E = np.mean(psi.bond_expectation_value(model.H_bonds))\n",
    "    if i % 10 == 9:\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 density in X = {mag_x:.5f}\".format(mag_x=mag_x))\n",
    "print(\"magnetization density in Z = {mag_z:.5f}\".format(mag_z=mag_z))\n",
    "E_exact = infinite_gs_energy(model.J, model.g)\n",
    "print(\"err in energy = {err:.3e}\".format(err=E - E_exact))"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "32c76202-8518-490c-a0a9-83915439baca",
   "metadata": {},
   "source": [
    "From the exercise, you should see that you need significantly more sweeps when the correlation length gets larger, in particular at the critical point! At the critical point, the [correlation length (of infinite MPS) scales](https://arxiv.org/abs/0812.2903) as $\\xi \\propto \\chi^\\kappa$, so you again need more sweeps to converge at larger bond dimensions."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "aaaa1454-b865-4e1a-a317-3f43644aebec",
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "markdown",
   "id": "1e99ab49",
   "metadata": {},
   "source": [
    "### Advanced exercises for the experts (and those who want to become them ;-) )\n",
    "\n",
    "- Obtain the ground state of the transverse field ising model at the critical point with DMRG for large `L`.\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",
    "\n",
    "\n",
    "\n",
    "\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "id": "8adcb517-0981-4faa-a756-1b792a1ee00f",
   "metadata": {},
   "outputs": [],
   "source": [
    "# At the critical point, correlations decay like a power law.\n",
    "# An MPS can only approximate powerlaws by sums of (decaying) exponentials, \n",
    "# that decay too fast at long distances.\n",
    "# In practice, increasing the bond dimension allows to approximate the power laws better and better, so one can still use DMRG."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "119170d8-d2bf-4d5b-b799-a08574dc7e37",
   "metadata": {},
   "source": [
    "- Compare running DMRG and imaginary time evolution with TEBD from `tenpy_toycodes/c_tebd.py` \n",
    "  for various parameters of `L`, `J`, `g`, and `bc`. Which one is faster? Do they always agree?"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "id": "5f1aabfc-7a3d-4450-a1fa-d94f8f2d73fe",
   "metadata": {},
   "outputs": [],
   "source": [
    "# imaginary time evolution is significantly slower than the variational DMRG ansatz\n",
    "# They can give different results e.g. in the symmetry broken phase, \n",
    "# where TEBD might return a symmetric superposition (cat state), \n",
    "# while DMRG tends to break the symmetries.\n"
   ]
  },
  {
   "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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