chern.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Calculating Chern number"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "from numpy import linalg as la\n",
    "\n",
    "O = 0.\n",
    "M = 1. # g\n",
    "C = 1. # N/m\n",
    "w0 = np.sqrt(C / M)\n",
    "l = 1. # distance between masses\n",
    "x = np.array([[1.], [0.]]) # x hat\n",
    "y = np.array([[0.], [1.]]) # y hat\n",
    "a1 = np.sqrt(3) * l * x\n",
    "a2 = (np.sqrt(3) * x + 3 * y) * l / 2.\n",
    "R1 = 1 / 3 * (a1 + a2)\n",
    "R2 = 1 / 3 * (-2 * a1 + a2)\n",
    "R3 = 1 / 3 * (a1 - 2 * a2)\n",
    "R11 = R1 * R1.conj().T\n",
    "R22 = R2 * R2.conj().T\n",
    "R33 = R3 * R3.conj().T"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 34,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 432x288 with 2 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "import numpy as np\n",
    "precision = 0.1\n",
    "kxs = np.arange(-np.pi, np.pi, precision) \n",
    "kys = np.arange(-np.pi, np.pi, precision)\n",
    "\n",
    "\n",
    "\n",
    "R0_ = lambda k: (1 / 2 * (3 - np.exp(1.j * k.dot(R1)) - np.exp(1.j * k.dot(R2)) - np.exp(1.j * k.dot(R3)))).item()\n",
    "R1_ = lambda k: (np.sqrt(3) / 4 * (np.exp(1.j * k.dot(R2)) - np.exp(1.j * k.dot(R1)))).item()\n",
    "R2_ = lambda k: (2 * O / w0**2).item()\n",
    "R3_ = lambda k: (1 / 4 * (1 - np.exp(1.j * k.dot(R1)) - np.exp(1.j * k.dot(R2)) + np.exp(1.j * k.dot(R3)))).item()\n",
    "R = lambda k: np.sqrt(R1_(k)**2 + R2_(k)**2 + R3_(k)**2)\n",
    "\n",
    "\n",
    "ws = np.zeros((len(kys), len(kxs), 2))\n",
    "\n",
    "for y, ky in enumerate(kys):\n",
    "    for x, kx in enumerate(kxs):\n",
    "        k = np.array([kx, ky])\n",
    "        ws[y, x] = np.sqrt(np.array([R0_(k) - R(k), R0_(k) + R(k)])).real\n",
    "        # ws[y, x] = np.array([R0_(k) - R(k), R0_(k) + R(k)]).real\n",
    "\n",
    "\n",
    "\n",
    "# 3D dispersion\n",
    "import matplotlib.pyplot as plt\n",
    "fig = plt.figure()\n",
    "ax = fig.add_subplot(111, projection='3d')\n",
    "X, Y = np.meshgrid(kxs, kys)\n",
    "\n",
    "vmax = np.amax(ws[:, :, 1])\n",
    "ax.plot_surface(X, Y, ws[:, :, 0], cmap='gist_rainbow_r') \n",
    "p = ax.plot_surface(X, Y, ws[:, :, 1], cmap='gist_rainbow_r') \n",
    "\n",
    "# ax.set_xlabel(r\"$k_x$ [/m]\", fontsize=14)\n",
    "# ax.set_xlim(-xw, xw)\n",
    "# ax.set_ylabel(r\"$k_y$ [/m]\", fontsize=14)\n",
    "# ax.set_ylim(-yw, yw)\n",
    "# ax.set_zlabel(r\"$\\omega$ [/s]\", fontsize=14)\n",
    "# ax.set_zlim(0)\n",
    "\n",
    "fig.colorbar(p, pad=0.15)\n",
    "# fig.savefig(\"2d-graphene-dispersion-3d.png\")\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 29,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "C:\\Users\\cfr2a\\AppData\\Local\\Temp/ipykernel_16020/4031708621.py:23: RuntimeWarning: invalid value encountered in sqrt\n",
      "  ax.plot_surface(X, Y, np.sqrt(evals_all[:, :, 0]), vmin=0., vmax=vmax, cmap='gist_rainbow_r')\n",
      "C:\\Users\\cfr2a\\AppData\\Local\\Temp/ipykernel_16020/4031708621.py:23: UserWarning: Z contains NaN values. This may result in rendering artifacts.\n",
      "  ax.plot_surface(X, Y, np.sqrt(evals_all[:, :, 0]), vmin=0., vmax=vmax, cmap='gist_rainbow_r')\n"
     ]
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 432x288 with 2 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "evals_all = np.zeros((len(kys), len(kxs), 2))\n",
    "for y, ky in enumerate(kys):\n",
    "    for x, kx in enumerate(kxs):\n",
    "        k = np.array([kx, ky])\n",
    "        H = np.array([\n",
    "            [R0_(k) + R3_(k), R1_(k) - 1.j * R2_(k)],\n",
    "            [R1_(k) + 1.j * R2_(k), R0_(k) - R3_(k)],\n",
    "        ])\n",
    "        evals, _ = la.eigh(H)\n",
    "        evals = evals[np.argsort(evals)]\n",
    "        evals_all[y, x] = evals\n",
    "evals_all = np.array(evals_all)\n",
    "\n",
    "\n",
    "\n",
    "# 3D dispersion\n",
    "import matplotlib.pyplot as plt\n",
    "fig = plt.figure()\n",
    "ax = fig.add_subplot(111, projection='3d')\n",
    "X, Y = np.meshgrid(kxs, kys)\n",
    "\n",
    "vmax = np.amax(np.sqrt(evals_all[:, :, 1]))\n",
    "ax.plot_surface(X, Y, np.sqrt(evals_all[:, :, 0]), vmin=0., vmax=vmax, cmap='gist_rainbow_r') \n",
    "p = ax.plot_surface(X, Y, np.sqrt(evals_all[:, :, 1]), vmin=0., vmax=vmax, cmap='gist_rainbow_r') \n",
    "\n",
    "# ax.set_xlabel(r\"$k_x$ [/m]\", fontsize=14)\n",
    "# ax.set_xlim(-xw, xw)\n",
    "# ax.set_ylabel(r\"$k_y$ [/m]\", fontsize=14)\n",
    "# ax.set_ylim(-yw, yw)\n",
    "# ax.set_zlabel(r\"$\\omega$ [/s]\", fontsize=14)\n",
    "# ax.set_zlim(0)\n",
    "\n",
    "fig.colorbar(p, pad=0.15)\n",
    "# fig.savefig(\"2d-graphene-dispersion-3d.png\")\n",
    "plt.show()\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Using library"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 36,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\n",
      "+----------------------------------------------------------------------+\n",
      "| ===================                                                  |\n",
      "| SURFACE CALCULATION                                                  |\n",
      "| ===================                                                  |\n",
      "| starting at 2022-01-26 08:47:02,460                                  |\n",
      "| running Z2Pack version 2.2.0                                         |\n",
      "|                                                                      |\n",
      "| gap_tol:            0.3                                              |\n",
      "| init_result:        None                                             |\n",
      "| iterator:           range(8, 27, 2)                                  |\n",
      "| load:               False                                            |\n",
      "| load_quiet:         True                                             |\n",
      "| min_neighbour_dist: 0.01                                             |\n",
      "| move_tol:           0.3                                              |\n",
      "| num_lines:          11                                               |\n",
      "| pos_tol:            0.01                                             |\n",
      "| save_file:          None                                             |\n",
      "| serializer:         auto                                             |\n",
      "| surface:            <function <lambda> at 0x000001F41A408310>        |\n",
      "| system:             <z2pack.hm.System object at 0x000001F4167FCA00>  |\n",
      "+----------------------------------------------------------------------+\n",
      "\n",
      "INFO: Adding lines required by 'num_lines'.\n",
      "INFO: Adding line at t = 0.0\n",
      "INFO:       Calculating line for N = 8\n",
      "INFO:       Calculating line for N = 10\n",
      "INFO: Adding line at t = 0.1\n",
      "INFO:       Calculating line for N = 8\n",
      "INFO:       Calculating line for N = 10\n",
      "INFO: Adding line at t = 0.2\n",
      "INFO:       Calculating line for N = 8\n",
      "INFO:       Calculating line for N = 10\n",
      "INFO: Adding line at t = 0.30000000000000004\n",
      "INFO:       Calculating line for N = 8\n",
      "INFO:       Calculating line for N = 10\n",
      "INFO: Adding line at t = 0.4\n",
      "INFO:       Calculating line for N = 8\n",
      "INFO:       Calculating line for N = 10\n",
      "INFO: Adding line at t = 0.5\n",
      "INFO:       Calculating line for N = 8\n",
      "INFO:       Calculating line for N = 10\n",
      "INFO: Adding line at t = 0.6000000000000001\n",
      "INFO:       Calculating line for N = 8\n",
      "INFO:       Calculating line for N = 10\n",
      "INFO: Adding line at t = 0.7000000000000001\n",
      "INFO:       Calculating line for N = 8\n",
      "INFO:       Calculating line for N = 10\n",
      "INFO: Adding line at t = 0.8\n",
      "INFO:       Calculating line for N = 8\n",
      "INFO:       Calculating line for N = 10\n",
      "INFO: Adding line at t = 0.9\n",
      "INFO:       Calculating line for N = 8\n",
      "INFO:       Calculating line for N = 10\n",
      "INFO: Adding line at t = 1.0\n",
      "INFO:       Calculating line for N = 8\n",
      "INFO:       Calculating line for N = 10\n",
      "INFO: Convergence criteria fulfilled for 10 of 10 neighbouring lines.\n",
      "\n",
      "+----------------------------------------------------------------------+\n",
      "|                   Calculation finished in 0h 0m 0s                   |\n",
      "+----------------------------------------------------------------------+\n",
      "+----------------------------------------------------------------------+\n",
      "|                         ==================                           |\n",
      "|                         CONVERGENCE REPORT                           |\n",
      "|                         ==================                           |\n",
      "|                                                                      |\n",
      "|                         Line Convergence                             |\n",
      "|                         ================                             |\n",
      "|                                                                      |\n",
      "|                             PosCheck                                 |\n",
      "|                             --------                                 |\n",
      "|                             PASSED: 11 of 11                         |\n",
      "|                                                                      |\n",
      "|                         Surface Convergence                          |\n",
      "|                         ===================                          |\n",
      "|                                                                      |\n",
      "|                             GapCheck                                 |\n",
      "|                             --------                                 |\n",
      "|                             PASSED: 10 of 10                         |\n",
      "|                                                                      |\n",
      "|                             MoveCheck                                |\n",
      "|                             ---------                                |\n",
      "|                             PASSED: 10 of 10                         |\n",
      "+----------------------------------------------------------------------+\n",
      "0.001234504501752204\n"
     ]
    }
   ],
   "source": [
    "import z2pack\n",
    "import numpy as np\n",
    "\n",
    "O = 13\n",
    "M = .01 # kg\n",
    "C = 4. # N/m\n",
    "w0 = np.sqrt(C / M)\n",
    "l = 1. # distance between masses\n",
    "x = np.array([[1.], [0.]]) # x hat\n",
    "y = np.array([[0.], [1.]]) # y hat\n",
    "a1 = np.sqrt(3) * l * x\n",
    "a2 = (np.sqrt(3) * x + 3 * y) * l / 2.\n",
    "R1 = 1 / 3 * (a1 + a2)\n",
    "R2 = 1 / 3 * (-2 * a1 + a2)\n",
    "R3 = 1 / 3 * (a1 - 2 * a2)\n",
    "R1h = R1 / la.norm(R1)\n",
    "R2h = R2 / la.norm(R2)\n",
    "R3h = R3 / la.norm(R3)\n",
    "R11 = R1h * R1h.conj().T\n",
    "R22 = R2h * R2h.conj().T\n",
    "R33 = R3h * R3h.conj().T\n",
    "Rw = np.array([[0., -1.], [1., 0.]])\n",
    "\n",
    "R0_ = lambda k: (1 / 2 * (3 - np.exp(1.j * k.dot(R1)) - np.exp(1.j * k.dot(R2)) - np.exp(1.j * k.dot(R3)))).item()\n",
    "R1_ = lambda k: (np.sqrt(3) / 4 * (np.exp(1.j * k.dot(R2)) - np.exp(1.j * k.dot(R1)))).item()\n",
    "R2_ = lambda k: (2 * O / w0**2).item()\n",
    "R3_ = lambda k: (1 / 4 * (1 - np.exp(1.j * k.dot(R1)) - np.exp(1.j * k.dot(R2)) + np.exp(1.j * k.dot(R3)))).item()\n",
    "R = lambda k: np.sqrt(R1_(k)**2 + R2_(k)**2 + R3_(k)**2)\n",
    "\n",
    "\n",
    "mu = -5.\n",
    "\n",
    "R0_ = lambda k: 0\n",
    "R1_ = lambda k: (-2 * np.sin(k[0])).item()\n",
    "R2_ = lambda k: (-2 * np.sin(k[1])).item()\n",
    "R3_ = lambda k: (2 * (np.cos(k[0]) + np.cos(k[1])) + mu).item()\n",
    "\n",
    "\n",
    "Os = np.arange(0, 100, 0.1)\n",
    "\n",
    "\n",
    "def hamiltonian(k):\n",
    "    kx, ky, kz = k\n",
    "    k_ = np.array([kx, ky])\n",
    "    p = np.exp(1.j * k_.dot(a1))\n",
    "    s = np.exp(1.j * k_.dot(a2))\n",
    "    # p = k_.dot(a1)\n",
    "    # s = k_.dot(a2)\n",
    "\n",
    "    H = np.array([\n",
    "        [R0_(k_) + R3_(k_), R1_(k_) - 1.j * R2_(k_)],\n",
    "        [R1_(k_) + 1.j * R2_(k_), R0_(k_) - R3_(k_)],\n",
    "    ])\n",
    "\n",
    "    # H = w0**2 * np.vstack([\n",
    "    #     np.hstack([R11 + R22 + R33 - 2.j * O * Rw / w0**2, -(R11 + R22 * p.conj() + R33 * s.conj())]),\n",
    "    #     np.hstack([-(R11 + R22 * p + R33 * s) ,R11 + R22 + R33 - 2.j * O * Rw / w0**2]),\n",
    "    # ])\n",
    "\n",
    "\n",
    "    return H\n",
    "system = z2pack.hm.System(hamiltonian)\n",
    "\n",
    "\n",
    "result = z2pack.surface.run(\n",
    "    system=system,\n",
    "    surface=lambda t1, t2: [t1, t2, 0]\n",
    ")\n",
    "\n",
    "print(z2pack.invariant.chern(result))   # Prints the Chern number\n",
    "# print(z2pack.invariant.z2(result))   # Prints the Chern numbe"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[[0.75      0.4330127]\n",
      " [0.4330127 0.25     ]] [[ 0.75      -0.4330127]\n",
      " [-0.4330127  0.25     ]] [[ 0. -0.]\n",
      " [-0.  1.]]\n"
     ]
    }
   ],
   "source": [
    "import numpy as np\n",
    "import numpy.linalg as la\n",
    "from sympy import symbols, Matrix, BlockMatrix, conjugate\n",
    "from sympy.functions import exp\n",
    "\n",
    "\n",
    "kx, ky = symbols('kx ky')\n",
    "\n",
    "\n",
    "O = 0.\n",
    "M = .01 # kg\n",
    "C = 4. # N/m\n",
    "w0 = np.sqrt(C / M)\n",
    "l = 1. # distance between masses\n",
    "x = np.array([[1.], [0.]]) # x hat\n",
    "y = np.array([[0.], [1.]]) # y hat\n",
    "a1 = np.sqrt(3) * l * x\n",
    "a2 = (np.sqrt(3) * x + 3 * y) * l / 2.\n",
    "R1 = 1 / 3 * (a1 + a2)\n",
    "R2 = 1 / 3 * (-2 * a1 + a2)\n",
    "R3 = 1 / 3 * (a1 - 2 * a2)\n",
    "R1h = R1 / la.norm(R1)\n",
    "R2h = R2 / la.norm(R2)\n",
    "R3h = R3 / la.norm(R3)\n",
    "R11 = R1h * R1h.conj().T\n",
    "R22 = R2h * R2h.conj().T\n",
    "R33 = R3h * R3h.conj().T\n",
    "Rw = np.array([[0., -1.], [1., 0.]])\n",
    "\n",
    "p = exp(1.j * np.sqrt(3) * kx)\n",
    "s = exp(1.j * (np.sqrt(3) * kx + 3 * ky) / 2)\n",
    "\n",
    "H = BlockMatrix([\n",
    "    [Matrix(R11 + R22 + R33 - 2.j * O * Rw / w0**2), Matrix(-(R11 + R22 * conjugate(p) + R33 * conjugate(s)))],\n",
    "    [Matrix(-(R11 + R22 * p + R33 * s)) ,Matrix(R11 + R22 + R33 - 2.j * O * Rw / w0**2)]\n",
    "])\n",
    "H = w0 ** 2 * Matrix(H)\n",
    "# H.eigenvects()\n",
    "print(R11, R22, R33)\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Chern with extended eigen vecs"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 47,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "(838, 726, 8) (838, 726, 8, 8)\n"
     ]
    }
   ],
   "source": [
    "import numpy as np\n",
    "import numpy.linalg as la\n",
    "\n",
    "\n",
    "O = 0.\n",
    "C = 1.\n",
    "M = 1.\n",
    "w0 = np.sqrt(C / M)\n",
    "a = 1. # distance between masses\n",
    "x = np.array([[1.], [0.]]) # x hat\n",
    "y = np.array([[0.], [1.]]) # y hat\n",
    "a1 = np.sqrt(3) * a * x\n",
    "a2 = (np.sqrt(3) * x + 3 * y) * a / 2.\n",
    "R1 = 1 / 3 * (a1 + a2)\n",
    "R2 = 1 / 3 * (-2 * a1 + a2)\n",
    "R3 = 1 / 3 * (a1 - 2 * a2)\n",
    "R1h = R1 / la.norm(R1)\n",
    "R2h = R2 / la.norm(R2)\n",
    "R3h = R3 / la.norm(R3)\n",
    "R11 = R1h * R1h.conj().T\n",
    "R22 = R2h * R2h.conj().T\n",
    "R33 = R3h * R3h.conj().T\n",
    "Rw = np.array([[0., -1.], [1., 0.]])\n",
    "precision = 0.01\n",
    "xw = np.pi / np.sqrt(3) * 2 # width of x\n",
    "yw = np.pi / 3 * 4 # width of y\n",
    "kxs = np.arange(-xw, xw, precision)\n",
    "kys = np.arange(-yw, yw, precision)\n",
    "\n",
    "\n",
    "evals_all = np.zeros((len(kys), len(kxs), 8), dtype=np.complex128)\n",
    "evecs_all = np.zeros((len(kys), len(kxs), 8, 8), dtype=np.complex128)\n",
    "for y, ky in enumerate(kys):\n",
    "    for x, kx in enumerate(kxs):\n",
    "        k = np.array([kx, ky])\n",
    "        p = np.exp(1.j * k.dot(a1))\n",
    "        s = np.exp(1.j * k.dot(a2))\n",
    "        L11 = np.vstack([\n",
    "            np.hstack([R11 + R22 + R33, -(R11 + p.conj() * R22 + s.conj() * R33)]),\n",
    "            np.hstack([-(R11 + p * R22 + s * R33), R11 + R22 + R33])\n",
    "        ])\n",
    "        L12 = np.vstack([\n",
    "            np.hstack([-Rw * 2.j * O, np.zeros((2, 2))]),\n",
    "            np.hstack([np.zeros((2, 2)), -Rw * 2.j * O])\n",
    "        ])\n",
    "        L = w0 ** 2 * np.vstack([\n",
    "            np.hstack([L11, L12]),\n",
    "            np.hstack([np.zeros((4, 4)), np.eye(4)])\n",
    "        ])\n",
    "        M = np.vstack([\n",
    "            np.hstack([np.zeros((4, 4)), np.eye(4)]),\n",
    "            np.hstack([np.eye(4), np.zeros((4, 4))])\n",
    "        ])\n",
    "\n",
    "        H = np.linalg.inv(M).dot(L)\n",
    "        evals, evecs = la.eig(H)\n",
    "        idcs = np.argsort(evals)\n",
    "        evals, evecs = evals[idcs], evecs[idcs]\n",
    "        evals_all[y, x] = evals\n",
    "        evecs_all[y, x] = evecs\n",
    "evals_all = np.array(evals_all)\n",
    "evecs_all = np.array(evecs_all)\n",
    "print(evals_all.shape, evecs_all.shape)\n",
    "\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 52,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "0.01\n",
      "False\n",
      "(101933.18741767509-101933.18741767509j)\n"
     ]
    }
   ],
   "source": [
    "from shapely.geometry import Point\n",
    "from shapely.geometry.polygon import Polygon\n",
    "\n",
    "x = np.array([[1.], [0.]]) # x hat\n",
    "y = np.array([[0.], [1.]]) # y hat\n",
    "a1_ = 2 * np.pi / np.sqrt(3) / a * (x - y / np.sqrt(3)) \n",
    "a2_ = 4 * np.pi / 3 / a * y\n",
    "K = (a1_ / 2 + a2_ / 4) / np.cos(np.pi / 6)**2\n",
    "b1 = 2 * np.pi / np.sqrt(3) / a * (x - y / np.sqrt(3))\n",
    "b2 = 4 * np.pi / 3 / a * y\n",
    "\n",
    "h = precision\n",
    "bz= Polygon([K, -K + b1 + b2, K - b1, -K, K - b1 - b2, -K + b1])\n",
    "\n",
    "print(h)\n",
    "print(bz.contains(Point(-4,0)))\n",
    "\n",
    "C = 0\n",
    "band_number = 6\n",
    "\n",
    "# xi = evecs_all[:, :, band_number, :2]\n",
    "# eta = evecs_all[:, :, band_number, 2:4]\n",
    "xi = evecs_all[:, :, :2, band_number]\n",
    "eta = evecs_all[:, :, 2:4, band_number]\n",
    "for y, ky in enumerate(kys):\n",
    "    for x, kx in enumerate(kxs):\n",
    "        p = Point(kx, ky)\n",
    "        if not bz.contains(p):\n",
    "            continue\n",
    "        dxi_dkx = (xi[y, x+1] - xi[y, x-1]) / (2 * h)\n",
    "        dxi_dky = (xi[y+1, x] - xi[y-1, x]) / (2 * h)\n",
    "        C += 1.j * dxi_dkx.conj().T.dot(dxi_dky) - dxi_dky.conj().T.dot(dxi_dkx)\n",
    "\n",
    "        deta_dkx = (eta[y, x+1] - eta[y, x-1]) / (2 * h)\n",
    "        deta_dky = (eta[y+1, x] - eta[y-1, x]) / (2 * h)\n",
    "        C += 1.j * deta_dkx.conj().T.dot(deta_dky) - deta_dky.conj().T.dot(deta_dkx)\n",
    "\n",
    "C /= 2 * np.pi\n",
    "# print(evecs_all[0, 0, 0, :4])\n",
    "# print(evecs_all[0, 0, 0, 4:])\n",
    "\n",
    "print(C)\n",
    "\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 56,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([-37.36966799,   1.81470808,  -6.64135569,  -1.35299878])"
      ]
     },
     "execution_count": 56,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "\n",
    "def calc_chern(hVec):\n",
    "    \"\"\"Calculate 1st Chern number given eigen-vectors. Using Japanese algorithm\n",
    "    (2005).\n",
    "    :param hVec: eigen-vectors of all band (assuming gapless).\n",
    "    :return: list of Chern number of all bands. Should summed to 0.\n",
    "    \"\"\"\n",
    "    hVec = np.array(hVec)\n",
    "    dimy, dimx, nlevels, _ = hVec.shape\n",
    "    cnlist = np.zeros(nlevels)\n",
    "\n",
    "    for iy in range(dimy-1):\n",
    "        for ix in range(dimx-1):\n",
    "            u12 = hVec[iy, ix + 1].conjugate().T @ hVec[iy, ix]\n",
    "            u23 = hVec[iy + 1, ix + 1].conjugate().T @ hVec[iy, ix + 1]\n",
    "            u34 = hVec[iy + 1, ix].conjugate().T @ hVec[iy + 1, ix + 1]\n",
    "            u41 = hVec[iy, ix].conjugate().T @ hVec[iy + 1, ix]\n",
    "            t12 = np.diag(u12.diagonal())\n",
    "            t23 = np.diag(u23.diagonal())\n",
    "            t34 = np.diag(u34.diagonal())\n",
    "            t41 = np.diag(u41.diagonal())\n",
    "            tplaquet = t41 @ t34 @ t23 @ t12\n",
    "            cnlist += np.angle(tplaquet.diagonal())\n",
    "\n",
    "    cnlist /= 2 * np.pi\n",
    "    cnlist = chop(cnlist)\n",
    "    return cnlist\n",
    "\n",
    "\n",
    "def chop(array, tol=1e-7):\n",
    "    \"\"\"Realize Mathematica Chop[].\n",
    "    :param array: 1D array.\n",
    "    :param tol: tolerance to be chopped. default to 1e-7\n",
    "    :return: chopped array. (original array alse modified.)\n",
    "    \"\"\"\n",
    "    for i in range(len(array)):\n",
    "        a = array[i]\n",
    "        if np.abs(a-round(a)) < tol:\n",
    "            array[i] = round(a)\n",
    "    return array\n",
    "\n",
    "calc_chern(evecs_all[:, :, :4, 4:])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Chern with perturbation"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 74,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "(838, 726, 4) (838, 726, 4, 4)\n"
     ]
    }
   ],
   "source": [
    "import numpy as np\n",
    "import numpy.linalg as la\n",
    "\n",
    "\n",
    "\n",
    "O = 4\n",
    "C = 4\n",
    "M = 0.01\n",
    "w0 = np.sqrt(C / M)\n",
    "a = 1. # distance between masses\n",
    "x = np.array([[1.], [0.]]) # x hat\n",
    "y = np.array([[0.], [1.]]) # y hat\n",
    "a1 = np.sqrt(3) * a * x\n",
    "a2 = (np.sqrt(3) * x + 3 * y) * a / 2.\n",
    "R1 = 1 / 3 * (a1 + a2)\n",
    "R2 = 1 / 3 * (-2 * a1 + a2)\n",
    "R3 = 1 / 3 * (a1 - 2 * a2)\n",
    "R1h = R1 / la.norm(R1)\n",
    "R2h = R2 / la.norm(R2)\n",
    "R3h = R3 / la.norm(R3)\n",
    "R11 = R1h * R1h.conj().T\n",
    "R22 = R2h * R2h.conj().T\n",
    "R33 = R3h * R3h.conj().T\n",
    "Rw = np.array([[0., -1.], [1., 0.]])\n",
    "precision = 1e-2\n",
    "xw = np.pi / np.sqrt(3) * 2 # width of x\n",
    "yw = np.pi / 3 * 4 # width of y\n",
    "kxs = np.arange(-xw, xw, precision)\n",
    "kys = np.arange(-yw, yw, precision)\n",
    "\n",
    "\n",
    "evals_all = np.zeros((len(kys), len(kxs), 4), dtype=np.complex128)\n",
    "evecs_all = np.zeros((len(kys), len(kxs), 4, 4), dtype=np.complex128)\n",
    "for y, ky in enumerate(kys):\n",
    "    for x, kx in enumerate(kxs):\n",
    "        k = np.array([kx, ky])\n",
    "        p = np.exp(1.j * k.dot(a1))\n",
    "        s = np.exp(1.j * k.dot(a2))\n",
    "        H = w0**2 * np.vstack([\n",
    "            np.hstack([R11 + R22 + R33 - 2.j * O * Rw / w0**2, -(R11 + R22 * p.conj() + R33 * s.conj())]),\n",
    "            np.hstack([-(R11 + R22 * p + R33 * s) ,R11 + R22 + R33 - 2.j * O * Rw / w0**2]),\n",
    "        ])\n",
    "        evals, evecs = la.eigh(H)\n",
    "        idcs = np.argsort(evals)\n",
    "        evals, evecs = evals[idcs], evecs[idcs]\n",
    "        evals_all[y, x] = evals\n",
    "        evecs_all[y, x] = evecs\n",
    "evals_all = np.array(evals_all)\n",
    "evecs_all = np.array(evecs_all)\n",
    "print(evals_all.shape, evecs_all.shape)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "ename": "KeyboardInterrupt",
     "evalue": "",
     "output_type": "error",
     "traceback": [
      "\u001b[1;31m---------------------------------------------------------------------------\u001b[0m",
      "\u001b[1;31mKeyboardInterrupt\u001b[0m                         Traceback (most recent call last)",
      "\u001b[1;32m~\\AppData\\Local\\Temp/ipykernel_16916/2554284660.py\u001b[0m in \u001b[0;36m<module>\u001b[1;34m\u001b[0m\n\u001b[0;32m     23\u001b[0m \u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m     24\u001b[0m     \u001b[1;31m# Construct wavenumber dataset\u001b[0m\u001b[1;33m\u001b[0m\u001b[1;33m\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[1;32m---> 25\u001b[1;33m     \u001b[0mwn\u001b[0m \u001b[1;33m=\u001b[0m \u001b[0mWaveNumber\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mWaveNumberType\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0mXY\u001b[0m\u001b[1;33m,\u001b[0m \u001b[0mlattice\u001b[0m\u001b[1;33m,\u001b[0m \u001b[0mprecision\u001b[0m\u001b[1;33m=\u001b[0m\u001b[1;36m3e-3\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0m\u001b[0;32m     26\u001b[0m     \u001b[0mwn_gkm\u001b[0m \u001b[1;33m=\u001b[0m \u001b[0mWaveNumber\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mWaveNumberType\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0mGKM\u001b[0m\u001b[1;33m,\u001b[0m \u001b[0mlattice\u001b[0m\u001b[1;33m,\u001b[0m \u001b[0mprecision\u001b[0m\u001b[1;33m=\u001b[0m\u001b[1;36m1e-1\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m     27\u001b[0m     \u001b[0mwn_generator\u001b[0m \u001b[1;33m=\u001b[0m \u001b[0mDataLoader\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mwn\u001b[0m\u001b[1;33m,\u001b[0m \u001b[1;33m**\u001b[0m\u001b[0mparams\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n",
      "\u001b[1;32mg:\\My Drive\\Documents\\School\\卒論\\mechanical-lattice\\conut\\data.py\u001b[0m in \u001b[0;36m__init__\u001b[1;34m(self, wn_type, lattice, precision)\u001b[0m\n\u001b[0;32m     22\u001b[0m             \u001b[0mself\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0mkys\u001b[0m \u001b[1;33m=\u001b[0m \u001b[0mtorch\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0marange\u001b[0m\u001b[1;33m(\u001b[0m\u001b[1;33m-\u001b[0m\u001b[0mlattice\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0myw\u001b[0m\u001b[1;33m,\u001b[0m \u001b[0mlattice\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0myw\u001b[0m\u001b[1;33m,\u001b[0m \u001b[0mprecision\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m     23\u001b[0m             \u001b[1;32mfor\u001b[0m \u001b[0my\u001b[0m\u001b[1;33m,\u001b[0m \u001b[0mky\u001b[0m \u001b[1;32min\u001b[0m \u001b[0menumerate\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mself\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0mkys\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m:\u001b[0m\u001b[1;33m\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[1;32m---> 24\u001b[1;33m                 \u001b[1;32mfor\u001b[0m \u001b[0mx\u001b[0m\u001b[1;33m,\u001b[0m \u001b[0mkx\u001b[0m \u001b[1;32min\u001b[0m \u001b[0menumerate\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mself\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0mkxs\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m:\u001b[0m\u001b[1;33m\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0m\u001b[0;32m     25\u001b[0m                     \u001b[0mks\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0mappend\u001b[0m\u001b[1;33m(\u001b[0m\u001b[1;33m[\u001b[0m\u001b[1;33m[\u001b[0m\u001b[0mkx\u001b[0m\u001b[1;33m]\u001b[0m\u001b[1;33m,\u001b[0m \u001b[1;33m[\u001b[0m\u001b[0mky\u001b[0m\u001b[1;33m]\u001b[0m\u001b[1;33m]\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m     26\u001b[0m                     \u001b[0midcs\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0mappend\u001b[0m\u001b[1;33m(\u001b[0m\u001b[1;33m[\u001b[0m\u001b[0my\u001b[0m\u001b[1;33m,\u001b[0m \u001b[0mx\u001b[0m\u001b[1;33m]\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n",
      "\u001b[1;32m~\\anaconda3\\lib\\site-packages\\torch\\_tensor.py\u001b[0m in \u001b[0;36m__iter__\u001b[1;34m(self)\u001b[0m\n\u001b[0;32m    646\u001b[0m                           \u001b[1;34m'iterations executed (and might lead to errors or silently give '\u001b[0m\u001b[1;33m\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m    647\u001b[0m                           'incorrect results).', category=torch.jit.TracerWarning, stacklevel=2)\n\u001b[1;32m--> 648\u001b[1;33m         \u001b[1;32mreturn\u001b[0m \u001b[0miter\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mself\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0munbind\u001b[0m\u001b[1;33m(\u001b[0m\u001b[1;36m0\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0m\u001b[0;32m    649\u001b[0m \u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m    650\u001b[0m     \u001b[1;32mdef\u001b[0m \u001b[0m__hash__\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mself\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m:\u001b[0m\u001b[1;33m\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n",
      "\u001b[1;31mKeyboardInterrupt\u001b[0m: "
     ]
    }
   ],
   "source": [
    "from conut import MechanicalGraphene, HamiltonianType, MechanicalGrapheneLattice\n",
    "from conut.data import WaveNumber, WaveNumberType\n",
    "from torch.utils.data import DataLoader\n",
    "import torch\n",
    "import numpy as np\n",
    "from shapely.geometry import Polygon, Point\n",
    "\n",
    "\n",
    "dev = 'cuda' if torch.cuda.is_available() else 'cpu'\n",
    "dev = 'cpu'\n",
    "κ = 1.\n",
    "α = 1.\n",
    "m = 1.\n",
    "l = 1.\n",
    "params = {'batch_size': 512,\n",
    "          'shuffle': False,\n",
    "          'num_workers': 4}\n",
    "\n",
    "for Ω in [0., 0.1, 0.2, 0.3, 0.4, 0.5, 0.6]:\n",
    "\n",
    "    # Setup Lattice\n",
    "    lattice = MechanicalGrapheneLattice(l, α, device=dev)\n",
    "\n",
    "    # Construct wavenumber dataset\n",
    "    wn = WaveNumber(WaveNumberType.XY, lattice, precision=3e-3)\n",
    "    wn_gkm = WaveNumber(WaveNumberType.GKM, lattice, precision=1e-1)\n",
    "    wn_generator = DataLoader(wn, **params)\n",
    "    wn_gkm_generator = DataLoader(wn_gkm, **params)\n",
    "\n",
    "    # Build mechanical graphene model\n",
    "    mg = MechanicalGraphene(κ=κ, m=m, α=α, lattice=lattice, h_type=HamiltonianType.Bulk, shape=wn.shape, Ω=Ω, perturbation=True).to(dev)\n",
    "    # mg_gkm = MechanicalGraphene(κ=κ, m=m, α=α, lattice=lattice, h_type=HamiltonianType.Bulk, shape=wn_gkm.shape, Ω=Ω, GKM=True, perturbation=False).to(dev)\n",
    "\n",
    "\n",
    "    for idcs_batch, ks_batch in wn_generator:\n",
    "        idcs_batch, ks_batch = idcs_batch.to(dev), ks_batch.to(dev)\n",
    "        mg(idcs_batch, ks_batch)\n",
    "    evecs = mg.evecs.detach().numpy()\n",
    "\n",
    "    def calc_chern(hVec):\n",
    "        \"\"\"Calculate 1st Chern number given eigen-vectors. Using Japanese algorithm\n",
    "        (2005).\n",
    "        :param hVec: eigen-vectors of all band (assuming gapless).\n",
    "        :return: list of Chern number of all bands. Should summed to 0.\n",
    "        \"\"\"\n",
    "        hVec = np.array(hVec)\n",
    "        dimy, dimx, nlevels, _ = hVec.shape\n",
    "        cnlist = np.zeros(nlevels)\n",
    "\n",
    "        for iy in range(dimy-1):\n",
    "            for ix in range(dimx-1):\n",
    "                u12 = hVec[iy, ix + 1].conjugate().T @ hVec[iy, ix]\n",
    "                u23 = hVec[iy + 1, ix + 1].conjugate().T @ hVec[iy, ix + 1]\n",
    "                u34 = hVec[iy + 1, ix].conjugate().T @ hVec[iy + 1, ix + 1]\n",
    "                u41 = hVec[iy, ix].conjugate().T @ hVec[iy + 1, ix]\n",
    "                t12 = np.diag(u12.diagonal())\n",
    "                t23 = np.diag(u23.diagonal())\n",
    "                t34 = np.diag(u34.diagonal())\n",
    "                t41 = np.diag(u41.diagonal())\n",
    "                tplaquet = t41 @ t34 @ t23 @ t12\n",
    "                cnlist += np.angle(tplaquet.diagonal())\n",
    "\n",
    "        cnlist /= 2 * np.pi\n",
    "        cnlist = chop(cnlist)\n",
    "        return cnlist\n",
    "\n",
    "\n",
    "    def chop(array, tol=1e-7):\n",
    "        \"\"\"Realize Mathematica Chop[].\n",
    "        :param array: 1D array.\n",
    "        :param tol: tolerance to be chopped. default to 1e-7\n",
    "        :return: chopped array. (original array alse modified.)\n",
    "        \"\"\"\n",
    "        for i in range(len(array)):\n",
    "            a = array[i]\n",
    "            if np.abs(a-round(a)) < tol:\n",
    "                array[i] = round(a)\n",
    "        return array\n",
    "\n",
    "    \n",
    "    x = np.array([[1.], [0.]]) # x hat\n",
    "    y = np.array([[0.], [1.]]) # y hat\n",
    "    a1_ = 2 * np.pi / np.sqrt(3) / l * (x - y / np.sqrt(3)) \n",
    "    a2_ = 4 * np.pi / 3 / l * y\n",
    "    K = (a1_ / 2 + a2_ / 4) / np.cos(np.pi / 6)**2\n",
    "    b1 = 2 * np.pi / np.sqrt(3) / l * (x - y / np.sqrt(3))\n",
    "    b2 = 4 * np.pi / 3 / l * y\n",
    "\n",
    "    bz= Polygon([K, -K + b1 + b2, K - b1, -K, K - b1 - b2, -K + b1])\n",
    "\n",
    "    evecs_all_bz = np.zeros((len(wn.kys), len(wn.kxs), 4, 4), dtype=np.complex128)\n",
    "\n",
    "    for y, ky in enumerate(wn.kys):\n",
    "        for x, kx in enumerate(wn.kxs):\n",
    "            p = Point(kx, ky)\n",
    "            if not bz.contains(p):\n",
    "                continue\n",
    "            evecs_all_bz[y, x] = evecs[y, x]\n",
    "\n",
    "    print(Ω, calc_chern(evecs_all_bz))"
   ]
  }
 ],
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