Test.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "This book is for the first edition of Kitaev Honeycombs in TeNPy."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 72,
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "import matplotlib.pyplot as plt"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 73,
   "metadata": {},
   "outputs": [],
   "source": [
    "from tenpy.networks.site import Site, SpinHalfFermionSite, SpinHalfSite, GroupedSite, SpinSite\n",
    "from tenpy.tools.misc import to_iterable, to_iterable_of_len, inverse_permutation\n",
    "from tenpy.networks.mps import MPS  # only to check boundary conditions\n",
    "\n",
    "from tenpy.models.lattice import Lattice, _parse_sites, Honeycomb\n",
    "from tenpy.models.model import CouplingMPOModel, NearestNeighborModel\n",
    "from tenpy.tools.params import get_parameter"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 74,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 2 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "import tenpy\n",
    "from tenpy.models import lattice\n",
    "from tenpy.algorithms import dmrg\n",
    "\n",
    "Lx, Ly = 3, 3\n",
    "fig, axes = plt.subplots(1, 2, sharex=True, sharey=True, figsize=(6, 4))\n",
    "\n",
    "reg_lat = lattice.Honeycomb(Lx=Lx, Ly=Ly, sites=None, bc='periodic')\n",
    "irr_lat = lattice.IrregularLattice(reg_lat, remove=[[0, 0, 0], [-1, -1, 1]])\n",
    "\n",
    "for lat, label, ax in zip([reg_lat, irr_lat],\n",
    "                          [\"regular\", \"irregular\"],\n",
    "                          axes.flatten()):\n",
    "    lat.plot_coupling(ax)\n",
    "    lat.plot_order(ax, linestyle=':')\n",
    "    lat.plot_sites(ax)\n",
    "    ax.set_aspect('equal')\n",
    "    ax.set_title(label)\n",
    "\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 504x576 with 4 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "Lx, Ly = 3, 3\n",
    "fig, axes = plt.subplots(2, 2, figsize=(7, 8))\n",
    "\n",
    "lat1 = lattice.Honeycomb(Lx, Ly, sites=None, bc='periodic')  # default order\n",
    "lat2 = lattice.Honeycomb(Lx, Ly, sites=None, bc='periodic',\n",
    "                        order=\"Cstyle\")  # first method to change order\n",
    "# alternative: directly set \"Cstyle\" order\n",
    "lat3 = lattice.Honeycomb(Lx, Ly, sites=None, bc='periodic')\n",
    "lat3.order = lat2.ordering(\"Cstyle\")  # now equivalent to lat2\n",
    "\n",
    "# general: can apply arbitrary permutation to the order\n",
    "lat4 = lattice.Honeycomb(Lx, Ly, sites=None, bc='periodic',\n",
    "                        order=\"Cstyle\")\n",
    "old_order = lat4.order\n",
    "permutation = []\n",
    "for i in range(0, len(old_order), 2):\n",
    "    permutation.append(i+1)\n",
    "    permutation.append(i)\n",
    "lat4.order = old_order[permutation, :]\n",
    "\n",
    "for lat, label, ax in zip([lat1, lat2, lat3, lat4],\n",
    "                          [\"order='default'\",\n",
    "                           \"order='Cstyle'\",\n",
    "                           \"order='Cstyle'\",\n",
    "                           \"custom permutation\"],\n",
    "                          axes.flatten()):\n",
    "    lat.plot_coupling(ax)\n",
    "    lat.plot_sites(ax)\n",
    "    lat.plot_order(ax, linestyle=':', linewidth=2.)\n",
    "    ax.set_aspect('equal')\n",
    "    ax.set_title('order = ' + repr(label))\n",
    "\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "ename": "NameError",
     "evalue": "name 'SpinSite' is not defined",
     "output_type": "error",
     "traceback": [
      "\u001b[0;31m---------------------------------------------------------------------------\u001b[0m",
      "\u001b[0;31mNameError\u001b[0m                                 Traceback (most recent call last)",
      "\u001b[0;32m<ipython-input-4-24881b7b7d28>\u001b[0m in \u001b[0;36m<module>\u001b[0;34m\u001b[0m\n\u001b[1;32m      2\u001b[0m \u001b[0mfig\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0maxes\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mplt\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0msubplots\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;36m2\u001b[0m\u001b[0;34m,\u001b[0m\u001b[0;36m1\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mfigsize\u001b[0m\u001b[0;34m=\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;36m7\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0;36m8\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m      3\u001b[0m \u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m----> 4\u001b[0;31m \u001b[0ms\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mSpinSite\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mS\u001b[0m\u001b[0;34m=\u001b[0m\u001b[0;36m0.5\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mconserve\u001b[0m\u001b[0;34m=\u001b[0m\u001b[0;32mNone\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m      5\u001b[0m lat2 = lattice.Honeycomb(Lx, Ly, sites=[s, s], bc=['open', 0],\n\u001b[1;32m      6\u001b[0m                         order=\"Cstyle\")  # first method to change order\n",
      "\u001b[0;31mNameError\u001b[0m: name 'SpinSite' is not defined"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 504x576 with 2 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "Lx, Ly = 5, 3\n",
    "fig, axes = plt.subplots(2,1, figsize=(7, 8))\n",
    "\n",
    "s = SpinSite(S=0.5, conserve=None)\n",
    "lat2 = lattice.Honeycomb(Lx, Ly, sites=[s, s], bc=['open', 0],\n",
    "                        order=\"Cstyle\")  # first method to change order\n",
    "for lat, label, ax in zip([lat2],\n",
    "                          [\"order='Cstyle'\"],\n",
    "                          axes.flatten()):\n",
    "    lat.plot_coupling(ax)\n",
    "    lat.plot_sites(ax)\n",
    "    lat.plot_order(ax, linestyle=':', linewidth=2.)\n",
    "    ax.set_aspect('equal')\n",
    "    ax.set_title('order = ' + repr(label))\n",
    "\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 40,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "{'nearest_neighbors': [(0, 1, array([0, 0])),\n",
       "  (1, 0, array([1, 0])),\n",
       "  (1, 0, array([0, 1]))],\n",
       " 'next_nearest_neighbors': [(0, 0, array([1, 0])),\n",
       "  (0, 0, array([0, 1])),\n",
       "  (0, 0, array([ 1, -1])),\n",
       "  (1, 1, array([1, 0])),\n",
       "  (1, 1, array([0, 1])),\n",
       "  (1, 1, array([ 1, -1]))],\n",
       " 'next_next_nearest_neighbors': [(1, 0, array([1, 1])),\n",
       "  (0, 1, array([-1,  1])),\n",
       "  (0, 1, array([ 1, -1]))],\n",
       " 'fourth_nearest_neighbors': [(0, 1, array([0, 1])),\n",
       "  (0, 1, array([1, 0])),\n",
       "  (0, 1, array([ 1, -2])),\n",
       "  (0, 1, array([ 0, -2])),\n",
       "  (0, 1, array([-2,  0])),\n",
       "  (0, 1, array([-2,  1]))],\n",
       " 'fifth_nearest_neighbors': [(0, 0, array([1, 1])),\n",
       "  (0, 0, array([ 2, -1])),\n",
       "  (0, 0, array([-1,  2])),\n",
       "  (1, 1, array([1, 1])),\n",
       "  (1, 1, array([ 2, -1])),\n",
       "  (1, 1, array([-1,  2]))]}"
      ]
     },
     "execution_count": 40,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "lat2.pairs"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "So for the default honeycomb in tenpy we can see that the bonds of nn are aligned as follows:\n",
    " - Jz\n",
    " - Jy\n",
    " - Jx"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [],
   "source": [
    "class KitaevHoneycombModel(CouplingMPOModel):\n",
    "    \"\"\"\n",
    "        Defining the MPO for Kitaev Honeycomb\n",
    "    \"\"\"\n",
    "    def __init__(self, model_params):\n",
    "        CouplingMPOModel.__init__(self, model_params)\n",
    "\n",
    "    def init_sites(self, model_params):\n",
    "        # conserve = get_parameter(model_params, 'conserve', None, self.name)\n",
    "        conserve = model_params.get('conserve', None)\n",
    "        S = model_params.get('S', 0.5) # by default spin one half\n",
    "        fs = SpinSite(S=S, conserve=conserve)\n",
    "        iSy = np.real(1.j*fs.get_op('Sy').to_ndarray())\n",
    "        fs.add_op('iSy', iSy)\n",
    "        return [fs, fs]\n",
    "\n",
    "    def init_lattice(self, model_params):\n",
    "        Lx = model_params.get('Lx', 4) # 2 is the least possible number for L to be a Kitaev ladder we want, and 4 is more secured (I hope so)\n",
    "        Ly = model_params.get('Ly', 3)\n",
    "        \n",
    "        gs = self.init_sites(model_params)\n",
    "        model_params.pop(\"Lx\")\n",
    "        model_params.pop(\"Ly\")\n",
    "\n",
    "\n",
    "        order = model_params.get('order', 'Cstyle')\n",
    "        bc = model_params.get('bc', 'periodic')\n",
    "        shift = model_params.get('shift', 0)\n",
    "        bc_MPS=model_params.get('bc_MPS', 'finite')\n",
    "        lattice_params = dict(\n",
    "            order=order,\n",
    "            bc=[bc, shift],\n",
    "            bc_MPS=bc_MPS,\n",
    "            basis=None,\n",
    "            positions=None,\n",
    "            nearest_neighbors=None,\n",
    "            next_nearest_neighbors=None,\n",
    "            next_next_nearest_neighbors=None,\n",
    "            pairs={},\n",
    "        )\n",
    "\n",
    "#         lat = KitaevLadderSnakeCompact(L, gs, **lattice_params)\n",
    "        lat = Honeycomb(Lx, Ly, sites=gs, **lattice_params)\n",
    "        return lat\n",
    "\n",
    "    def init_terms(self, model_params):\n",
    "        # Jx = get_parameter(model_params, 'Jx', 1., self.name, True)\n",
    "        # Jy = get_parameter(model_params, 'Jy', 1., self.name, True)\n",
    "        # Jz = get_parameter(model_params, 'Jz', 1., self.name, True)\n",
    "        Jx = model_params.get('Jx', 1.)\n",
    "        Jy = model_params.get('Jy', 1.)\n",
    "        Jz = model_params.get('Jz', 1.)\n",
    "\n",
    "        u1, u2, dx = self.lat.pairs['nearest_neighbors'][0]\n",
    "        self.add_coupling(Jz, u1, 'Sz', u2, 'Sz', dx)\n",
    "        u1, u2, dx = self.lat.pairs['nearest_neighbors'][1]\n",
    "        self.add_coupling(-Jy, u1, 'iSy', u2, 'iSy', dx)\n",
    "        u1, u2, dx = self.lat.pairs['nearest_neighbors'][2]\n",
    "        self.add_coupling(Jx, u1, 'Sx', u2, 'Sx', dx)\n",
    "#         for u1, u2, dx in self.lat.pairs['nearest_neighbors_y']:\n",
    "#             self.add_coupling(Jy, u1, 'Sy', u2, 'Sy', dx)         \n",
    "#         for u1, u2, dx in self.lat.pairs['nearest_neighbors_z']:\n",
    "#             self.add_coupling(Jz, u1, 'Sz', u2, 'Sz', dx)\n",
    "        "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 56,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Reading 'Lx'=4 for config KitaevHoneycombModel\n",
      "Reading 'Ly'=3 for config KitaevHoneycombModel\n",
      "Reading 'conserve'=None for config KitaevHoneycombModel\n",
      "Reading 'S'=0.5 for config KitaevHoneycombModel\n",
      "Reading 'order'='Cstyle' for config KitaevHoneycombModel\n",
      "Reading 'bc'='periodic' for config KitaevHoneycombModel\n",
      "Reading 'bc_MPS'='infinite' for config KitaevHoneycombModel\n",
      "Reading 'Jx'=1.0 for config KitaevHoneycombModel\n",
      "Reading 'Jy'=1.0 for config KitaevHoneycombModel\n",
      "Reading 'Jz'=1.0 for config KitaevHoneycombModel\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/home/jerry/anaconda3/lib/python3.7/site-packages/tenpy/tools/params.py:225: UserWarning: unused option ['dtype'] for config KitaevHoneycombModel\n",
      "\n",
      "  warnings.warn(msg.format(keys=sorted(unused), name=self.name))\n"
     ]
    }
   ],
   "source": [
    "Jx = 1.0\n",
    "Jy = 1.0\n",
    "Jz = 1.0\n",
    "S = 0.5\n",
    "order='Cstyle'\n",
    "Lx = 4\n",
    "Ly = 3\n",
    "\n",
    "verbose=True\n",
    "bc='periodic'\n",
    "bc_MPS='infinite'\n",
    "\n",
    "\n",
    "model_params = dict(\n",
    "    conserve=None, \n",
    "    Jx=Jx, \n",
    "    Jy=Jy, \n",
    "    Jz=Jz, \n",
    "    Lx=Lx, \n",
    "    Ly=Ly, \n",
    "    order='Cstyle',\n",
    "    S=S,\n",
    "    verbose=verbose,\n",
    "    bc=bc,\n",
    "    bc_MPS=bc_MPS,\n",
    "    dtype=float,\n",
    "    )\n",
    "\n",
    "M = KitaevHoneycombModel(model_params)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 44,
   "metadata": {},
   "outputs": [],
   "source": [
    "o = M.calc_H_MPO()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 45,
   "metadata": {},
   "outputs": [
    {
     "data": {
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     },
     "execution_count": 45,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "o.get_W(1).to_ndarray()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 96,
   "metadata": {},
   "outputs": [],
   "source": [
    "def run_atomic(\n",
    "    # model parameters\n",
    "    chi=30, \n",
    "    Jx=1., \n",
    "    Jy=1., \n",
    "    Jz=1., \n",
    "    S=.5, \n",
    "    Lx=4, \n",
    "    Ly=3, \n",
    "    bc='periodic', \n",
    "    shift=0,\n",
    "    bc_MPS='infinite', \n",
    "    conserve='parity',\n",
    "    order='Cstyle',\n",
    "    dtype=float,\n",
    "    ####### dmrg parameters #######\n",
    "    initial_psi=None, # input psi\n",
    "    initial='random', \n",
    "    max_E_err=1.e-6, \n",
    "    max_S_err=1.e-4, \n",
    "    max_sweeps=200, \n",
    "    N_sweeps_check=10, \n",
    "    canonicalized=True, \n",
    "    mixer=True,\n",
    "    mixer_params={\n",
    "        'amplitude': 1.e-4,\n",
    "        'decay': 1.2,\n",
    "        'disable_after': 50\n",
    "    },\n",
    "    trunc_params={\n",
    "        'chi_max': 4,\n",
    "        'svd_min': 1.e-10,\n",
    "    },\n",
    "    # control for the verbose output\n",
    "    verbose=1, \n",
    "):\n",
    "    \"\"\" \n",
    "        The fundamental function for running DMRG\n",
    "    \"\"\"\n",
    "\n",
    "    #######################\n",
    "    # set the paramters for model initialization\n",
    "    model_params = dict(\n",
    "        conserve=conserve, \n",
    "        Jx=Jx, \n",
    "        Jy=Jy, \n",
    "        Jz=Jz, \n",
    "        Lx=Lx, \n",
    "        Ly=Ly, \n",
    "        S=S,\n",
    "        verbose=verbose,\n",
    "        bc=bc,\n",
    "        bc_MPS=bc_MPS,\n",
    "        order=order,\n",
    "        dtype=dtype,\n",
    "        )\n",
    "    L = Lx*Ly\n",
    "    # initialize the model\n",
    "    M = KitaevHoneycombModel(model_params)\n",
    "    # providing a product state as the initial state\n",
    "    # prod_state = [\"up\", \"up\"] * (2 * model_params['L'])\n",
    "    # random generated initial state\n",
    "#     if initial_psi==None:\n",
    "#         prod_state = [ choice([\"up\", \"down\"]) for i in range(2 * L)]\n",
    "#         if initial == 'up':\n",
    "#             prod_state = [\"up\" for i in range(2 * L)]\n",
    "#         if initial == 'down':\n",
    "#             prod_state = [\"down\" for i in range(2 * L)]\n",
    "#         psi = MPS.from_product_state(\n",
    "#             M.lat.mps_sites(), \n",
    "#             prod_state, \n",
    "#             bc=M.lat.bc_MPS,\n",
    "#         )\n",
    "#     else:\n",
    "#         psi = initial_psi.copy()\n",
    "    #######################\n",
    "    prod_state = [\"up\"] * (2*L) \n",
    "#     prod_state[0] = \"down\"\n",
    "    psi = MPS.from_product_state(\n",
    "        M.lat.mps_sites(), \n",
    "        prod_state, \n",
    "        bc=M.lat.bc_MPS,\n",
    "    )\n",
    "    \n",
    "    #######################\n",
    "    # set the parameters for the dmrg routine\n",
    "    dmrg_params = {\n",
    "        'start_env': 10,\n",
    "#         'mixer': False,  # setting this to True helps to escape local minima\n",
    "        'mixer': mixer,\n",
    "        'mixer_params': mixer_params,\n",
    "        'trunc_params': trunc_params,\n",
    "        'max_E_err': max_E_err,\n",
    "        'max_S_err': max_S_err,\n",
    "        'max_sweeps': max_sweeps,\n",
    "        'N_sweeps_check': N_sweeps_check,\n",
    "        'verbose': verbose,\n",
    "    }\n",
    "    #######################\n",
    "    \n",
    "    if verbose:\n",
    "        print(\"\\n\")\n",
    "        print(\"=\" * 80)\n",
    "        print(\"=\"*30 + \"START\" + \"=\"*30)\n",
    "        print(\"=\" * 80)\n",
    "        print(\"Chi = \", chi, '\\n')\n",
    "\n",
    "    eng = dmrg.TwoSiteDMRGEngine(psi, M, dmrg_params)\n",
    "    eng.reset_stats()\n",
    "    eng.trunc_params['chi_max'] = chi\n",
    "    info = eng.run()\n",
    "\n",
    "    if canonicalized:\n",
    "        psi.canonical_form()\n",
    "        if verbose:\n",
    "            print(\"Before the canonicalization:\")\n",
    "            print(\"Bond dim = \", psi.chi)\n",
    "\n",
    "            print(\"Canonicalizing...\")\n",
    "            psi_before = psi.copy()\n",
    "\n",
    "\n",
    "        if verbose:\n",
    "            ov = psi.overlap(psi_before, charge_sector=0)\n",
    "            print(\"The norm is: \",psi.norm)\n",
    "            print(\"The overlap is: \", ov)\n",
    "            print(\"After the canonicalization:\")\n",
    "            print(\"Bond dim = \", psi.chi)\n",
    "\n",
    "        print(\"Computing properties\")\n",
    "\n",
    "    energy=info[0]\n",
    "\n",
    "    if verbose:\n",
    "        print(\"Optimizing\")\n",
    "\n",
    "    tenpy.tools.optimization.optimize(3)\n",
    "\n",
    "    if verbose:\n",
    "        print(\"Loop for chi=%d done.\" % chi)\n",
    "        print(\"=\" * 80)\n",
    "        print(\"=\"*30 + \" END \" + \"=\"*30)\n",
    "        print(\"=\" * 80)\n",
    "        \n",
    "    # the wave function, the ground-state energy, and the DMRG engine are all that we need\n",
    "    result = dict(\n",
    "        psi=psi.copy(),\n",
    "        energy=energy,\n",
    "        sweeps_stat=eng.sweep_stats.copy(),\n",
    "        parameters=dict(\n",
    "            # model parameters\n",
    "            chi=chi,\n",
    "            Jx=Jx, \n",
    "            Jy=Jy, \n",
    "            Jz=Jz, \n",
    "            L=L, \n",
    "            # dmrg parameters\n",
    "            initial_psi=initial_psi,\n",
    "            initial=initial,\n",
    "            max_E_err=max_E_err,\n",
    "            max_S_err=max_S_err,\n",
    "            max_sweeps=max_sweeps,\n",
    "        )\n",
    "    )\n",
    "    return result"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 87,
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Reading 'Lx'=4 for config KitaevHoneycombModel\n",
      "Reading 'Ly'=3 for config KitaevHoneycombModel\n",
      "Reading 'conserve'='parity' for config KitaevHoneycombModel\n",
      "Reading 'S'=0.5 for config KitaevHoneycombModel\n",
      "Reading 'order'='Cstyle' for config KitaevHoneycombModel\n",
      "Reading 'bc'='periodic' for config KitaevHoneycombModel\n",
      "Reading 'bc_MPS'='infinite' for config KitaevHoneycombModel\n",
      "Reading 'Jx'=1.0 for config KitaevHoneycombModel\n",
      "Reading 'Jy'=0.1 for config KitaevHoneycombModel\n",
      "Reading 'Jz'=1.0 for config KitaevHoneycombModel\n",
      "\n",
      "\n",
      "================================================================================\n",
      "==============================START==============================\n",
      "================================================================================\n",
      "Chi =  30 \n",
      "\n",
      "Subconfig 'trunc_params'=Config(<3 options>, 'trunc_params') for config TwoSiteDMRGEngine\n",
      "Initial sweeps...\n",
      "Reading 'start_env'=10 for config TwoSiteDMRGEngine\n",
      "Updating environment\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/home/jerry/anaconda3/lib/python3.7/site-packages/tenpy/tools/params.py:225: UserWarning: unused option ['dtype'] for config KitaevHoneycombModel\n",
      "\n",
      "  warnings.warn(msg.format(keys=sorted(unused), name=self.name))\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "..........\n",
      "Reading 'N_sweeps_check'=10 for config TwoSiteDMRGEngine\n",
      "Reading 'max_sweeps'=200 for config TwoSiteDMRGEngine\n",
      "Reading 'max_E_err'=1e-06 for config TwoSiteDMRGEngine\n",
      "Reading 'max_S_err'=0.0001 for config TwoSiteDMRGEngine\n",
      "Reading 'mixer'=True for config TwoSiteDMRGEngine\n",
      "Subconfig 'mixer_params'=Config(<4 options>, 'mixer_params') for config TwoSiteDMRGEngine\n"
     ]
    },
    {
     "ename": "KeyboardInterrupt",
     "evalue": "",
     "output_type": "error",
     "traceback": [
      "\u001b[0;31m---------------------------------------------------------------------------\u001b[0m",
      "\u001b[0;31mKeyboardInterrupt\u001b[0m                         Traceback (most recent call last)",
      "\u001b[0;32m<ipython-input-87-9dc2668acb65>\u001b[0m in \u001b[0;36m<module>\u001b[0;34m\u001b[0m\n\u001b[1;32m      4\u001b[0m     \u001b[0mJy\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0;36m0.1\u001b[0m\u001b[0;34m,\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m      5\u001b[0m     \u001b[0mJz\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0;36m1.0\u001b[0m\u001b[0;34m,\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m----> 6\u001b[0;31m     \u001b[0mshift\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0;36m0\u001b[0m\u001b[0;34m,\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m      7\u001b[0m )\n",
      "\u001b[0;32m<ipython-input-86-8132508fbf04>\u001b[0m in \u001b[0;36mrun_atomic\u001b[0;34m(chi, Jx, Jy, Jz, S, Lx, Ly, bc, shift, bc_MPS, conserve, order, dtype, initial_psi, initial, max_E_err, max_S_err, max_sweeps, N_sweeps_check, canonicalized, mixer, mixer_params, trunc_params, verbose)\u001b[0m\n\u001b[1;32m    109\u001b[0m     \u001b[0meng\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mreset_stats\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m    110\u001b[0m     \u001b[0meng\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mtrunc_params\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0;34m'chi_max'\u001b[0m\u001b[0;34m]\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mchi\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m--> 111\u001b[0;31m     \u001b[0minfo\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0meng\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mrun\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m    112\u001b[0m \u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m    113\u001b[0m     \u001b[0;32mif\u001b[0m \u001b[0mcanonicalized\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n",
      "\u001b[0;32m~/anaconda3/lib/python3.7/site-packages/tenpy/algorithms/dmrg.py\u001b[0m in \u001b[0;36mrun\u001b[0;34m(self)\u001b[0m\n\u001b[1;32m    337\u001b[0m             \u001b[0;31m# --------- the main work --------------\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m    338\u001b[0m             \u001b[0;32mfor\u001b[0m \u001b[0mi\u001b[0m \u001b[0;32min\u001b[0m \u001b[0mrange\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mN_sweeps_check\u001b[0m \u001b[0;34m-\u001b[0m \u001b[0;36m1\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m--> 339\u001b[0;31m                 \u001b[0mself\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0msweep\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mmeas_E_trunc\u001b[0m\u001b[0;34m=\u001b[0m\u001b[0;32mFalse\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m    340\u001b[0m             \u001b[0mmax_trunc_err\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mself\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0msweep\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mmeas_E_trunc\u001b[0m\u001b[0;34m=\u001b[0m\u001b[0;32mTrue\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m    341\u001b[0m             \u001b[0mmax_E_trunc\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mnp\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mmax\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mself\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mE_trunc_list\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n",
      "\u001b[0;32m~/anaconda3/lib/python3.7/site-packages/tenpy/algorithms/dmrg.py\u001b[0m in \u001b[0;36msweep\u001b[0;34m(self, optimize, meas_E_trunc)\u001b[0m\n\u001b[1;32m    743\u001b[0m         \u001b[0;31m# wrapper around tenpy.algorithms.mps_common.Sweep.sweep()\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m    744\u001b[0m         \u001b[0mself\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0m_meas_E_trunc\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mmeas_E_trunc\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m--> 745\u001b[0;31m         \u001b[0mres\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0msuper\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0msweep\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0moptimize\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m    746\u001b[0m         \u001b[0;32mif\u001b[0m \u001b[0moptimize\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m    747\u001b[0m             \u001b[0;31m# update mixer\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n",
      "\u001b[0;32m~/anaconda3/lib/python3.7/site-packages/tenpy/algorithms/mps_common.py\u001b[0m in \u001b[0;36msweep\u001b[0;34m(self, optimize)\u001b[0m\n\u001b[1;32m    298\u001b[0m             \u001b[0;31m# --------- the main work --------------\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m    299\u001b[0m             \u001b[0mtheta\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mself\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mprepare_update\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m--> 300\u001b[0;31m             \u001b[0mupdate_data\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mself\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mupdate_local\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mtheta\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0moptimize\u001b[0m\u001b[0;34m=\u001b[0m\u001b[0moptimize\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m    301\u001b[0m             \u001b[0;32mif\u001b[0m \u001b[0mupdate_LP\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m    302\u001b[0m                 \u001b[0mself\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mupdate_LP\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mupdate_data\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0;34m'U'\u001b[0m\u001b[0;34m]\u001b[0m\u001b[0;34m)\u001b[0m  \u001b[0;31m# (requires updated B)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n",
      "\u001b[0;32m~/anaconda3/lib/python3.7/site-packages/tenpy/algorithms/dmrg.py\u001b[0m in \u001b[0;36mupdate_local\u001b[0;34m(self, theta, optimize, meas_E_trunc)\u001b[0m\n\u001b[1;32m    884\u001b[0m         \u001b[0mage\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mself\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0menv\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mget_LP_age\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mi0\u001b[0m\u001b[0;34m)\u001b[0m \u001b[0;34m+\u001b[0m \u001b[0;36m2\u001b[0m \u001b[0;34m+\u001b[0m \u001b[0mself\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0menv\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mget_RP_age\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mi0\u001b[0m \u001b[0;34m+\u001b[0m \u001b[0;36m1\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m    885\u001b[0m         \u001b[0;32mif\u001b[0m \u001b[0moptimize\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m--> 886\u001b[0;31m             \u001b[0mE0\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mtheta\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mN\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mov_change\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mself\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mdiag\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mtheta\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m    887\u001b[0m         \u001b[0;32melse\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m    888\u001b[0m             \u001b[0mE0\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mN\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mov_change\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0;32mNone\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0;36m0\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0;36m0.\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n",
      "\u001b[0;32m~/anaconda3/lib/python3.7/site-packages/tenpy/algorithms/dmrg.py\u001b[0m in \u001b[0;36mdiag\u001b[0;34m(self, theta_guess)\u001b[0m\n\u001b[1;32m    604\u001b[0m                 \u001b[0mE\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mtheta\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mfull_diag_effH\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mself\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0meff_H\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mtheta_guess\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mkeep_sector\u001b[0m\u001b[0;34m=\u001b[0m\u001b[0;32mTrue\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m    605\u001b[0m             \u001b[0;32melse\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m--> 606\u001b[0;31m                 \u001b[0mE\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mtheta\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mN\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mlanczos\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mself\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0meff_H\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mtheta_guess\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mself\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mlanczos_params\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m    607\u001b[0m         \u001b[0;32melif\u001b[0m \u001b[0mself\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mdiag_method\u001b[0m \u001b[0;34m==\u001b[0m \u001b[0;34m'lanczos'\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m    608\u001b[0m             \u001b[0mE\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mtheta\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mN\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mlanczos\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mself\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0meff_H\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mtheta_guess\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mself\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mlanczos_params\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n",
      "\u001b[0;32m~/anaconda3/lib/python3.7/site-packages/tenpy/linalg/lanczos.py\u001b[0m in \u001b[0;36mlanczos\u001b[0;34m(H, psi, options, orthogonal_to)\u001b[0m\n\u001b[1;32m    397\u001b[0m         \u001b[0mSee\u001b[0m \u001b[0;34m:\u001b[0m\u001b[0mmeth\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;31m`\u001b[0m\u001b[0mLanczosGroundState\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mrun\u001b[0m\u001b[0;31m`\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m    398\u001b[0m     \"\"\"\n\u001b[0;32m--> 399\u001b[0;31m     \u001b[0;32mreturn\u001b[0m \u001b[0mLanczosGroundState\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mH\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mpsi\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0moptions\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0morthogonal_to\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mrun\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m    400\u001b[0m \u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m    401\u001b[0m \u001b[0;34m\u001b[0m\u001b[0m\n",
      "\u001b[0;32m~/anaconda3/lib/python3.7/site-packages/tenpy/linalg/lanczos.py\u001b[0m in \u001b[0;36mrun\u001b[0;34m(self)\u001b[0m\n\u001b[1;32m    171\u001b[0m             \u001b[0mUsed\u001b[0m \u001b[0mdimension\u001b[0m \u001b[0mof\u001b[0m \u001b[0mthe\u001b[0m \u001b[0mKrylov\u001b[0m \u001b[0mspace\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mi\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0me\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mhow\u001b[0m \u001b[0mmany\u001b[0m \u001b[0miterations\u001b[0m \u001b[0mwhere\u001b[0m \u001b[0mperformed\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m    172\u001b[0m         \"\"\"\n\u001b[0;32m--> 173\u001b[0;31m         \u001b[0mN\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mself\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0m_calc_T\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m    174\u001b[0m         \u001b[0mE0\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mself\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mEs\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0mN\u001b[0m \u001b[0;34m-\u001b[0m \u001b[0;36m1\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0;36m0\u001b[0m\u001b[0;34m]\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m    175\u001b[0m         \u001b[0;32mif\u001b[0m \u001b[0mself\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mverbose\u001b[0m \u001b[0;34m>=\u001b[0m \u001b[0;36m1\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n",
      "\u001b[0;32m~/anaconda3/lib/python3.7/site-packages/tenpy/linalg/lanczos.py\u001b[0m in \u001b[0;36m_calc_T\u001b[0;34m(self)\u001b[0m\n\u001b[1;32m    199\u001b[0m             \u001b[0mw\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0miscale_prefactor\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;36m1.\u001b[0m \u001b[0;34m/\u001b[0m \u001b[0mbeta\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m    200\u001b[0m             \u001b[0mself\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0m_to_cache\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mw\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m--> 201\u001b[0;31m             \u001b[0mw\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mself\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mH\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mmatvec\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mw\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m    202\u001b[0m             \u001b[0malpha\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mnp\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mreal\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mnpc\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0minner\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mw\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mself\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0m_cache\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0;34m-\u001b[0m\u001b[0;36m1\u001b[0m\u001b[0;34m]\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0maxes\u001b[0m\u001b[0;34m=\u001b[0m\u001b[0;34m'range'\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mdo_conj\u001b[0m\u001b[0;34m=\u001b[0m\u001b[0;32mTrue\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mitem\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m    203\u001b[0m             \u001b[0mT\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0mk\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mk\u001b[0m\u001b[0;34m]\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0malpha\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n",
      "\u001b[0;32m~/anaconda3/lib/python3.7/site-packages/tenpy/algorithms/mps_common.py\u001b[0m in \u001b[0;36mmatvec\u001b[0;34m(self, theta)\u001b[0m\n\u001b[1;32m    718\u001b[0m             \u001b[0mtheta\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mnpc\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mtensordot\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mself\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mLP\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mtheta\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0maxes\u001b[0m\u001b[0;34m=\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0;34m'vR'\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0;34m'vL'\u001b[0m\u001b[0;34m]\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m    719\u001b[0m             \u001b[0mtheta\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mnpc\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mtensordot\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mself\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mW0\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mtheta\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0maxes\u001b[0m\u001b[0;34m=\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0;34m'wL'\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0;34m'p0*'\u001b[0m\u001b[0;34m]\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0;34m[\u001b[0m\u001b[0;34m'wR'\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0;34m'p0'\u001b[0m\u001b[0;34m]\u001b[0m\u001b[0;34m]\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m--> 720\u001b[0;31m             \u001b[0mtheta\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mnpc\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mtensordot\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mtheta\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mself\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mW1\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0maxes\u001b[0m\u001b[0;34m=\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0;34m'wR'\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0;34m'p1'\u001b[0m\u001b[0;34m]\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0;34m[\u001b[0m\u001b[0;34m'wL'\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0;34m'p1*'\u001b[0m\u001b[0;34m]\u001b[0m\u001b[0;34m]\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m    721\u001b[0m             \u001b[0mtheta\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mnpc\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mtensordot\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mtheta\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mself\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mRP\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0maxes\u001b[0m\u001b[0;34m=\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0;34m'wR'\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0;34m'vR'\u001b[0m\u001b[0;34m]\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0;34m[\u001b[0m\u001b[0;34m'wL'\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0;34m'vL'\u001b[0m\u001b[0;34m]\u001b[0m\u001b[0;34m]\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m    722\u001b[0m             \u001b[0mtheta\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mireplace_labels\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0;34m'vR*'\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0;34m'vL*'\u001b[0m\u001b[0;34m]\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0;34m[\u001b[0m\u001b[0;34m'vL'\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0;34m'vR'\u001b[0m\u001b[0;34m]\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n",
      "\u001b[0;32m~/anaconda3/lib/python3.7/site-packages/tenpy/linalg/np_conserved.py\u001b[0m in \u001b[0;36mtensordot\u001b[0;34m(a, b, axes)\u001b[0m\n\u001b[1;32m   3421\u001b[0m     \u001b[0;32melse\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m   3422\u001b[0m         \u001b[0;31m# #### the main work\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m-> 3423\u001b[0;31m         \u001b[0mres\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0m_tensordot_worker\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0ma\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mb\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0maxes\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m   3424\u001b[0m     \u001b[0;31m# labels\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m   3425\u001b[0m     \u001b[0mres\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0m_labels\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0m_drop_duplicate_labels\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0ma\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0m_labels\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m-\u001b[0m\u001b[0maxes\u001b[0m\u001b[0;34m]\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mb\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0m_labels\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0maxes\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m]\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n",
      "\u001b[0;31mKeyboardInterrupt\u001b[0m: "
     ]
    }
   ],
   "source": [
    "run_atomic(\n",
    "    S = 0.5,\n",
    "    Jx = 1.0,\n",
    "    Jy = 0.1,\n",
    "    Jz = 1.0,\n",
    "    shift = 0,\n",
    ")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Test on the MPO model"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 88,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Reading 'Lx'=2 for config KitaevHoneycombModel\n",
      "Reading 'Ly'=3 for config KitaevHoneycombModel\n",
      "Reading 'conserve'=None for config KitaevHoneycombModel\n",
      "Reading 'S'=0.5 for config KitaevHoneycombModel\n",
      "Reading 'order'='Cstyle' for config KitaevHoneycombModel\n",
      "Reading 'bc'='periodic' for config KitaevHoneycombModel\n",
      "Reading 'bc_MPS'='finite' for config KitaevHoneycombModel\n",
      "Reading 'Jx'=1.5 for config KitaevHoneycombModel\n",
      "Reading 'Jy'=1.0 for config KitaevHoneycombModel\n",
      "Reading 'Jz'=1.0 for config KitaevHoneycombModel\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/home/jerry/anaconda3/lib/python3.7/site-packages/tenpy/tools/params.py:225: UserWarning: unused option ['dtype'] for config KitaevHoneycombModel\n",
      "\n",
      "  warnings.warn(msg.format(keys=sorted(unused), name=self.name))\n"
     ]
    }
   ],
   "source": [
    "Jx = 1.5\n",
    "Jy = 1.0\n",
    "Jz = 1.0\n",
    "S = 0.5\n",
    "order='Cstyle'\n",
    "Lx = 2\n",
    "Ly = 3\n",
    "\n",
    "verbose=True\n",
    "bc='periodic'\n",
    "bc_MPS='finite'\n",
    "\n",
    "\n",
    "model_params = dict(\n",
    "    conserve=None, \n",
    "    Jx=Jx, \n",
    "    Jy=Jy, \n",
    "    Jz=Jz, \n",
    "    Lx=Lx, \n",
    "    Ly=Ly, \n",
    "    order='Cstyle',\n",
    "    S=S,\n",
    "    verbose=verbose,\n",
    "    bc=bc,\n",
    "    bc_MPS=bc_MPS,\n",
    "    dtype=float,\n",
    "    )\n",
    "\n",
    "M = KitaevHoneycombModel(model_params)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 89,
   "metadata": {},
   "outputs": [],
   "source": [
    "mpo = M.calc_H_MPO()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 90,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/home/jerry/anaconda3/lib/python3.7/site-packages/tenpy/tools/params.py:225: UserWarning: unused option ['dtype'] for config KitaevHoneycombModel\n",
      "\n",
      "  warnings.warn(msg.format(keys=sorted(unused), name=self.name))\n"
     ]
    }
   ],
   "source": [
    "ED = tenpy.algorithms.exact_diag.ExactDiag(M, max_size=1e8)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 91,
   "metadata": {},
   "outputs": [],
   "source": [
    "ED.build_full_H_from_mpo()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 92,
   "metadata": {},
   "outputs": [],
   "source": [
    "ED.full_diagonalization()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 93,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(-2.8913517829688593,\n",
       " <npc.Array shape=(4096,) charge=ChargeInfo([], []) labels=['ps']>)"
      ]
     },
     "execution_count": 93,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "ED.groundstate()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 97,
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Reading 'Lx'=2 for config KitaevHoneycombModel\n",
      "Reading 'Ly'=3 for config KitaevHoneycombModel\n",
      "Reading 'conserve'=None for config KitaevHoneycombModel\n",
      "Reading 'S'=0.5 for config KitaevHoneycombModel\n",
      "Reading 'order'='Cstyle' for config KitaevHoneycombModel\n",
      "Reading 'bc'='periodic' for config KitaevHoneycombModel\n",
      "Reading 'bc_MPS'='finite' for config KitaevHoneycombModel\n",
      "Reading 'Jx'=1.5 for config KitaevHoneycombModel\n",
      "Reading 'Jy'=1.0 for config KitaevHoneycombModel\n",
      "Reading 'Jz'=1.0 for config KitaevHoneycombModel\n",
      "\n",
      "\n",
      "================================================================================\n",
      "==============================START==============================\n",
      "================================================================================\n",
      "Chi =  128 \n",
      "\n",
      "Subconfig 'trunc_params'=Config(<3 options>, 'trunc_params') for config TwoSiteDMRGEngine\n",
      "Reading 'N_sweeps_check'=10 for config TwoSiteDMRGEngine\n",
      "Reading 'max_sweeps'=200 for config TwoSiteDMRGEngine\n",
      "Reading 'max_E_err'=1e-06 for config TwoSiteDMRGEngine\n",
      "Reading 'max_S_err'=0.0001 for config TwoSiteDMRGEngine\n",
      "Reading 'mixer'=True for config TwoSiteDMRGEngine\n",
      "Subconfig 'mixer_params'=Config(<4 options>, 'mixer_params') for config TwoSiteDMRGEngine\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/home/jerry/anaconda3/lib/python3.7/site-packages/tenpy/tools/params.py:225: UserWarning: unused option ['dtype'] for config KitaevHoneycombModel\n",
      "\n",
      "  warnings.warn(msg.format(keys=sorted(unused), name=self.name))\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "================================================================================\n",
      "sweep 10, age = 12\n",
      "Energy = -2.8913517829688518, S = nan, norm_err = 1.1e-12\n",
      "Current memory usage 1484.9 MB, time elapsed: 3.3 s\n",
      "Delta E = nan, Delta S = 0.0000e+00 (per sweep)\n",
      "max_trunc_err = 5.0018e-20, max_E_trunc = 3.9968e-15\n",
      "MPS bond dimensions: [2, 4, 8, 16, 32, 64, 32, 16, 8, 4, 2]\n",
      "================================================================================\n",
      "sweep 20, age = 12\n",
      "Energy = -2.8913517829688598, S = nan, norm_err = 3.9e-13\n",
      "Current memory usage 1484.9 MB, time elapsed: 6.4 s\n",
      "Delta E = -7.9936e-16, Delta S = 0.0000e+00 (per sweep)\n",
      "max_trunc_err = 3.7985e-20, max_E_trunc = 9.7700e-15\n",
      "MPS bond dimensions: [2, 4, 8, 16, 32, 64, 32, 16, 8, 4, 2]\n",
      "Convergence criterium reached with enabled mixer.\n",
      "disable mixer and continue\n",
      "================================================================================\n",
      "sweep 30, age = 12\n",
      "Energy = -2.8913517829688571, S = 1.7128460562441725, norm_err = 1.4e-14\n",
      "Current memory usage 1484.9 MB, time elapsed: 7.7 s\n",
      "Delta E = 2.6645e-16, Delta S = nan (per sweep)\n",
      "max_trunc_err = 0.0000e+00, max_E_trunc = 3.9968e-15\n",
      "MPS bond dimensions: [2, 4, 8, 16, 32, 64, 32, 16, 8, 4, 2]\n",
      "================================================================================\n",
      "sweep 40, age = 12\n",
      "Energy = -2.8913517829688562, S = 1.7128460562441719, norm_err = 3.4e-14\n",
      "Current memory usage 1484.9 MB, time elapsed: 9.0 s\n",
      "Delta E = 8.8818e-17, Delta S = -6.6613e-17 (per sweep)\n",
      "max_trunc_err = 0.0000e+00, max_E_trunc = 1.7764e-15\n",
      "MPS bond dimensions: [2, 4, 8, 16, 32, 64, 32, 16, 8, 4, 2]\n",
      "================================================================================\n",
      "DMRG finished after 40 sweeps.\n",
      "total size = 12, maximum chi = 64\n",
      "================================================================================\n",
      "Before the canonicalization:\n",
      "Bond dim =  [2, 4, 8, 16, 32, 64, 32, 16, 8, 4, 2]\n",
      "Canonicalizing...\n",
      "The norm is:  1.0\n",
      "The overlap is:  0.9999999999999987\n",
      "After the canonicalization:\n",
      "Bond dim =  [2, 4, 8, 16, 32, 64, 32, 16, 8, 4, 2]\n",
      "Computing properties\n",
      "Optimizing\n",
      "Loop for chi=128 done.\n",
      "================================================================================\n",
      "============================== END ==============================\n",
      "================================================================================\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/home/jerry/anaconda3/lib/python3.7/site-packages/tenpy/tools/params.py:225: UserWarning: unused option ['dtype'] for config KitaevHoneycombModel\n",
      "\n",
      "  warnings.warn(msg.format(keys=sorted(unused), name=self.name))\n",
      "/home/jerry/anaconda3/lib/python3.7/site-packages/tenpy/tools/params.py:225: UserWarning: unused option ['start_env'] for config TwoSiteDMRGEngine\n",
      "\n",
      "  warnings.warn(msg.format(keys=sorted(unused), name=self.name))\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "{'psi': <tenpy.networks.mps.MPS at 0x7f1dc0ac6ed0>,\n",
       " 'energy': -2.891351782968856,\n",
       " 'sweeps_stat': {'sweep': [10, 20, 30, 40],\n",
       "  'N_updates': [200, 400, 600, 800],\n",
       "  'E': [-2.8913517829688518,\n",
       "   -2.8913517829688598,\n",
       "   -2.891351782968857,\n",
       "   -2.891351782968856],\n",
       "  'S': [nan, nan, 1.7128460562441725, 1.7128460562441719],\n",
       "  'time': [3.3256094455718994,\n",
       "   6.386650562286377,\n",
       "   7.682952404022217,\n",
       "   9.004379272460938],\n",
       "  'max_trunc_err': [5.001753903765168e-20, 3.798450567047983e-20, 0.0, 0.0],\n",
       "  'max_E_trunc': [3.9968028886505635e-15,\n",
       "   9.769962616701378e-15,\n",
       "   3.9968028886505635e-15,\n",
       "   1.7763568394002505e-15],\n",
       "  'max_chi': [64, 64, 64, 64],\n",
       "  'norm_err': [1.1226215484275553e-12,\n",
       "   3.889577234355368e-13,\n",
       "   1.3705087397084555e-14,\n",
       "   3.4159998419500317e-14]},\n",
       " 'parameters': {'chi': 128,\n",
       "  'Jx': 1.5,\n",
       "  'Jy': 1.0,\n",
       "  'Jz': 1.0,\n",
       "  'L': 6,\n",
       "  'initial_psi': None,\n",
       "  'initial': 'random',\n",
       "  'max_E_err': 1e-06,\n",
       "  'max_S_err': 0.0001,\n",
       "  'max_sweeps': 200}}"
      ]
     },
     "execution_count": 97,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "model_params = dict(\n",
    "    conserve=None, \n",
    "    Jx=Jx, \n",
    "    Jy=Jy, \n",
    "    Jz=Jz, \n",
    "    Lx=Lx, \n",
    "    Ly=Ly, \n",
    "    order='Cstyle',\n",
    "    S=S,\n",
    "    verbose=verbose,\n",
    "    bc=bc,\n",
    "    bc_MPS=bc_MPS,\n",
    "    dtype=float,\n",
    "    chi=128,\n",
    "    )\n",
    "run_atomic(\n",
    "    **model_params\n",
    ")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 64,
   "metadata": {},
   "outputs": [],
   "source": [
    "Sx = np.array([[0., 0.5], [0.5, 0.]])\n",
    "iSy = np.array([[0., 0.5], [-0.5, 0.]])\n",
    "Sz = np.array([[0.5, 0.], [0., -0.5]])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 65,
   "metadata": {},
   "outputs": [],
   "source": [
    "import scipy\n",
    "from scipy import sparse\n",
    "from scipy.sparse.linalg import eigs, eigsh # use eigsh instead of eigs to speed up as well as to get real eigenvalues\n",
    "\n",
    "import numpy as np"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 102,
   "metadata": {},
   "outputs": [],
   "source": [
    "## the elementary Pauli matrices\n",
    "X = sparse.csr_matrix(Sx)\n",
    "Y = sparse.csr_matrix(iSy)\n",
    "Z = sparse.csr_matrix(Sz)\n",
    "I = sparse.eye(2)\n",
    "\n",
    "sigma_list = [I, X, Y, Z]\n",
    "\n",
    "# the function to generate the many-body onsite Pauli operators\n",
    "def Sigma(op_num, site, L):\n",
    "    assert op_num==0 or op_num==1 or op_num==2 or op_num==3\n",
    "    assert site>=0 and site<L\n",
    "    \n",
    "    op = sigma_list[op_num]\n",
    "    \n",
    "    if site==0:\n",
    "        return sparse.kron(op, sparse.csr_matrix(np.eye(2**(L-1))))\n",
    "    elif site==L-1:\n",
    "        return sparse.kron(sparse.csr_matrix(np.eye(2**(L-1))), op)\n",
    "    else: \n",
    "        IA = sparse.kron(sparse.csr_matrix(np.eye(2**(site))), op)\n",
    "        return sparse.kron(IA, sparse.csr_matrix(np.eye(2**(L-1-site))))\n",
    "\n",
    "def get_H_Kitaev_Honeycomb(\n",
    "    Jx, Jy, Jz, \n",
    "    Lx, Ly, # the number of unitcells\n",
    "    bc, # boundary condition\n",
    "    shift=0, # control the identity condition along the y direction\n",
    "    ):\n",
    "    # currently i've only implemented open and periodic boundary conditions\n",
    "    assert bc=='open' or bc=='periodic'\n",
    "\n",
    "    # parameter setting\n",
    "    unit_size = 2 # every unitcell is to be composed of 4 different spins\n",
    "    L = Lx * Ly * unit_size # total number of spin-1/2 site\n",
    "\n",
    "    H = sparse.csr_matrix((2**L, 2**L)) # initialize the sparse matrix for representing the Hamiltonian\n",
    "    \n",
    "    xbd, ybd, zbd = get_Honeycomb_bond(\n",
    "        Lx, Ly, \n",
    "        bc_x=bc, bc_y='periodic', \n",
    "        shift=shift,\n",
    "        order='Cstyle',\n",
    "    )\n",
    "    for x_coord in xbd:\n",
    "        site0 = x_coord[0]\n",
    "        site1 = x_coord[1]\n",
    "        Op0 = Sigma(1, site0, L=L)\n",
    "        Op1 = Sigma(1, site1, L=L)\n",
    "        H += Jx*Op0.dot(Op1)\n",
    "    for y_coord in ybd:\n",
    "        site0 = y_coord[0]\n",
    "        site1 = y_coord[1]\n",
    "        Op0 = Sigma(2, site0, L=L)\n",
    "        Op1 = Sigma(2, site1, L=L)\n",
    "        H += Jy*Op0.dot(Op1)\n",
    "    for z_coord in zbd:\n",
    "        site0 = z_coord[0]\n",
    "        site1 = z_coord[1]\n",
    "        Op0 = Sigma(3, site0, L=L)\n",
    "        Op1 = Sigma(3, site1, L=L)\n",
    "        H += Jz*Op0.dot(Op1)\n",
    "    \n",
    "    return H"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 103,
   "metadata": {},
   "outputs": [],
   "source": [
    "H = get_H_Kitaev_Honeycomb(Jx, Jy, Jz, Lx, Ly, bc, shift=0)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 104,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(array([-2.89135178, -2.89135178, -2.89135178, -2.89135178, -2.84220922,\n",
       "        -2.84220922]),\n",
       " array([[-2.72206471e-03, -5.64205669e-03, -7.91532124e-03,\n",
       "         -3.22663177e-03, -4.01201410e-03, -1.38797152e-03],\n",
       "        [ 6.61016345e-17,  1.21430643e-17, -3.28888070e-17,\n",
       "         -4.29095782e-17,  5.48659346e-03,  5.30502986e-03],\n",
       "        [-1.03832574e-16,  4.33680869e-17, -3.30656252e-17,\n",
       "          2.00769416e-16, -5.48659346e-03, -5.30502986e-03],\n",
       "        ...,\n",
       "        [-7.94761987e-17,  5.55111512e-17,  3.29788043e-17,\n",
       "          1.47860349e-16, -5.48659346e-03, -5.30502986e-03],\n",
       "        [ 7.83998997e-17, -1.73472348e-18,  3.38643772e-17,\n",
       "         -7.06651545e-17,  5.48659346e-03,  5.30502986e-03],\n",
       "        [-2.72206471e-03, -5.64205669e-03, -7.91532124e-03,\n",
       "         -3.22663177e-03, -4.01201410e-03, -1.38797152e-03]]))"
      ]
     },
     "execution_count": 104,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "scipy.sparse.linalg.eigsh(H, which='SA')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 58,
   "metadata": {},
   "outputs": [],
   "source": [
    "def get_Honeycomb_bond(\n",
    "    Lx, Ly, \n",
    "    bc_x='open', bc_y='periodic', \n",
    "    shift=0, # how the y-direction identification works, (x, y+N) = (x+shift, y)\n",
    "    order='Cstyle', # see tenpy's doc for the details of 'Cstyle'...\n",
    "):\n",
    "    \"\"\"\n",
    "        Given the parameters of honeycomb, define and return the bonds/edges list.\n",
    "    \"\"\"\n",
    "    assert bc_x in ['open', 'periodic']\n",
    "    assert bc_y in ['open', 'periodic']\n",
    "    x_bonds = set([])\n",
    "    y_bonds = set([])\n",
    "    z_bonds = set([])\n",
    "    \n",
    "    get_i = lambda x,y: (x*Ly + y) # the 1d pos for unicell\n",
    "#     def get_i(x, y):\n",
    "#         if bc_x=='open':\n",
    "#             assert 0 <= x < Lx\n",
    "#         if bc_y=='open':\n",
    "#             assert 0 <= y < Ly\n",
    "#         x_mod = x % Lx\n",
    "#         y_mod = y % Ly\n",
    "#         return (x_mod * Ly + y )\n",
    "    \n",
    "    # z bond\n",
    "    for lx in range(Lx):\n",
    "        for ly in range(Ly):\n",
    "            i0 = 2*get_i(lx, ly)\n",
    "            i1 = i0 + 1\n",
    "            bond = (i0, i1)\n",
    "            z_bonds.add(bond)\n",
    "    \n",
    "    # x bond\n",
    "    for lx in range(Lx):\n",
    "        for ly in range(Ly - 1):\n",
    "            i0 = 2*get_i(lx, ly) + 1\n",
    "            i1 = i0 + 1 # equivalent to `2*get_i(lx, ly + 1)`\n",
    "            bond = (i0, i1)\n",
    "            x_bonds.add(bond)\n",
    "    if bc_y == 'periodic':\n",
    "        ly = Ly - 1\n",
    "        for lx in range(Lx):\n",
    "            i0 = 2*get_i(lx, ly) + 1\n",
    "            i1 = 2*get_i(lx+shift, 0)\n",
    "            bond = (i0, i1)\n",
    "            x_bonds.add(bond)\n",
    "            \n",
    "    # y bond\n",
    "    for lx in range(Lx - 1):\n",
    "        for ly in range(Ly):\n",
    "            i0 = 2*get_i(lx, ly) + 1\n",
    "            i1 = 2*get_i(lx+1, ly)\n",
    "            bond = (i0, i1)\n",
    "            y_bonds.add(bond)\n",
    "    if bc_x == 'periodic':\n",
    "        lx = Lx - 1\n",
    "        for ly in range(Ly):\n",
    "            i0 = 2*get_i(lx, ly) + 1\n",
    "            i1 = 2*get_i(0, ly)\n",
    "            bond = (i0, i1)\n",
    "            y_bonds.add(bond)\n",
    "    \n",
    "    \n",
    "    return x_bonds, y_bonds, z_bonds"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 62,
   "metadata": {},
   "outputs": [],
   "source": [
    "xbd, ybc, zbd = get_Honeycomb_bond(\n",
    "    Lx, Ly, \n",
    "    bc_x='periodic', bc_y='periodic', \n",
    "    shift=0,\n",
    "    order='Cstyle',\n",
    ")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
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