{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Ground state search for 1D quantum Ising model"
   ]
  },
  {
   "attachments": {},
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "In this experiment we will use our DMRG optimiser to find the ground state\n",
    "of an open-bounded transverse field Ising chain. The Hamiltonian reads:\n",
    "$$\n",
    "H = - \\sum_{i=1}^{N-1} Z_i Z_{i+1} - h * \\sum_{i=1}^{N} X_i.\n",
    "$$\n",
    "Here, the magnetic field is in the units of the nearest-neighbour ZZ-interaction.\n",
    "We find the ground state of this Hamiltonian and compute some observables."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "import matplotlib.pyplot as plt\n",
    "import numpy as np\n",
    "from opt_einsum import contract\n",
    "from tqdm import tqdm\n",
    "from scipy.sparse.linalg import eigsh\n",
    "\n",
    "from ising import IsingExact, IsingMPO\n",
    "from mdopt.mps.utils import create_simple_product_state\n",
    "from mdopt.optimiser.dmrg import DMRG as dmrg"
   ]
  },
  {
   "attachments": {},
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Let us first check we build the right MPO. We do this by virtue of constructing a 3-site MPO and then changing it into the Hamiltonian."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Checking the exact and the MPO Hamiltonians being the same: True\n"
     ]
    }
   ],
   "source": [
    "NUM_SITES = 3\n",
    "H_MAGNETIC = 1.0\n",
    "ising_exact = IsingExact(num_sites=NUM_SITES, h_magnetic=H_MAGNETIC)\n",
    "ising_mpo = IsingMPO(num_sites=NUM_SITES, h_magnetic=H_MAGNETIC)\n",
    "ham_mpo = ising_mpo.hamiltonian_mpo()\n",
    "m = contract(\n",
    "    \"zabc, adef, dygh -> begcfh\",\n",
    "    ham_mpo[0],\n",
    "    ham_mpo[1],\n",
    "    ham_mpo[2],\n",
    "    optimize=[(0, 1), (0, 1)],\n",
    ").reshape((8, 8))\n",
    "\n",
    "print(\n",
    "    \"Checking the exact and the MPO Hamiltonians being the same:\",\n",
    "    (ising_exact.hamiltonian_dense() == m).all(),\n",
    ")"
   ]
  },
  {
   "attachments": {},
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Then, we solve the model by both exact diagonalisation and DMRG. Afterwards, we need to check that the ground states are the same up to a phase."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "DMRG running:\n",
      "\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "100%|██████████| 10/10 [00:20<00:00,  2.08s/it]\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\n",
      "Eigensolver running.\n",
      "The ground states are the same: True\n"
     ]
    }
   ],
   "source": [
    "NUM_SITES = 10\n",
    "H_MAGNETIC = 1.0\n",
    "NUM_DMRG_RUNS = 10\n",
    "CHI_MAX = 128\n",
    "CUT = 1e-12\n",
    "MODE = \"SA\"\n",
    "TOL = 1e-7\n",
    "ising_exact = IsingExact(num_sites=NUM_SITES, h_magnetic=H_MAGNETIC)\n",
    "ising_mpo = IsingMPO(num_sites=NUM_SITES, h_magnetic=H_MAGNETIC)\n",
    "ham_mpo = ising_mpo.hamiltonian_mpo()\n",
    "ham_sparse = ising_exact.hamiltonian_sparse()\n",
    "\n",
    "mps_start = create_simple_product_state(NUM_SITES, which=\"+\")\n",
    "\n",
    "print(\"DMRG running:\")\n",
    "print(\"\")\n",
    "engine = dmrg(mps_start, ham_mpo, chi_max=CHI_MAX, cut=CUT, mode=MODE)\n",
    "engine.run(NUM_DMRG_RUNS)\n",
    "print(\"\")\n",
    "ground_state_mps = engine.mps\n",
    "print(\"Eigensolver running.\")\n",
    "ground_state_exact = eigsh(ham_sparse, k=2, tol=TOL)[1][:, 0]\n",
    "print(\n",
    "    \"The ground states are the same:\",\n",
    "    np.isclose(abs(ground_state_mps.dense()), abs(ground_state_exact)).all(),\n",
    ")"
   ]
  },
  {
   "attachments": {},
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Now, we would like to compare the magnetisation plots from exact diagonalisation and DMRG. The plots should coincide exactly."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "100%|██████████| 20/20 [07:08<00:00, 21.44s/it]\n"
     ]
    }
   ],
   "source": [
    "transverse_magnetic_field_space = np.linspace(0.2, 2.0, 20)\n",
    "mag_z_exact = []\n",
    "mag_x_exact = []\n",
    "mag_z_dmrg = []\n",
    "mag_x_dmrg = []\n",
    "for magnetic_field in tqdm(transverse_magnetic_field_space):\n",
    "    ising_exact = IsingExact(num_sites=NUM_SITES, h_magnetic=magnetic_field)\n",
    "    ising_mpo = IsingMPO(num_sites=NUM_SITES, h_magnetic=magnetic_field)\n",
    "    ham_mpo = ising_mpo.hamiltonian_mpo()\n",
    "    ham_sparse = ising_exact.hamiltonian_sparse()\n",
    "    mps_start = create_simple_product_state(num_sites=NUM_SITES, which=\"+\")\n",
    "    engine = dmrg(mps_start, ham_mpo, chi_max=CHI_MAX, cut=CUT, mode=MODE, silent=True)\n",
    "    engine.run(NUM_DMRG_RUNS)\n",
    "    ground_state_mps = engine.mps\n",
    "    ground_state_exact = eigsh(ham_sparse, k=2, tol=TOL)[1][:, 0]\n",
    "\n",
    "    mag_z_exact.append(ising_exact.average_chain_z_magnetisation(ground_state_exact))\n",
    "    mag_x_exact.append(ising_exact.average_chain_x_magnetisation(ground_state_exact))\n",
    "\n",
    "    mag_z_dmrg.append(ising_mpo.average_chain_z_magnetisation(ground_state_mps))\n",
    "    mag_x_dmrg.append(ising_mpo.average_chain_x_magnetisation(ground_state_mps))"
   ]
  },
  {
   "attachments": {},
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Now we can take a look at the plots!"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 500x400 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 500x400 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.figure(figsize=(5, 4))\n",
    "plt.plot(transverse_magnetic_field_space, mag_z_exact, label=\"Exact\", linewidth=3)\n",
    "plt.plot(\n",
    "    transverse_magnetic_field_space,\n",
    "    mag_z_dmrg,\n",
    "    label=\"DMRG\",\n",
    "    linestyle=\"dashed\",\n",
    "    linewidth=3,\n",
    ")\n",
    "plt.xlabel(\"Transverse magnetic field $h$\")\n",
    "plt.ylabel(\"Longitudinal magnetisation $m_z$\", rotation=90, labelpad=10)\n",
    "plt.xlim((0.2, 2))\n",
    "plt.ylim((-1, 1))\n",
    "plt.legend(fontsize=10)\n",
    "plt.grid(True)\n",
    "plt.tight_layout()\n",
    "plt.show()\n",
    "\n",
    "plt.figure(figsize=(5, 4))\n",
    "plt.plot(transverse_magnetic_field_space, mag_x_exact, label=\"Exact\", linewidth=3)\n",
    "plt.plot(\n",
    "    transverse_magnetic_field_space,\n",
    "    mag_x_dmrg,\n",
    "    label=\"DMRG\",\n",
    "    linestyle=\"dashed\",\n",
    "    linewidth=3,\n",
    ")\n",
    "plt.xlabel(\"Transverse magnetic field $h$\")\n",
    "plt.ylabel(\"Transverse magnetisation $m_x$\", rotation=90, labelpad=10)\n",
    "plt.xlim((0.2, 2))\n",
    "plt.ylim((0, 1))\n",
    "plt.legend(fontsize=10)\n",
    "plt.grid(True)\n",
    "plt.tight_layout()\n",
    "plt.show()"
   ]
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "mdopt-ZdbamFdU-py3.10",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.10.16"
  },
  "orig_nbformat": 4
 },
 "nbformat": 4,
 "nbformat_minor": 2
}