{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 1,
   "id": "cb509096-42c6-4a45-8dc4-a8eed3116e67",
   "metadata": {
    "tags": []
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Intel MKL WARNING: Support of Intel(R) Streaming SIMD Extensions 4.2 (Intel(R) SSE4.2) enabled only processors has been deprecated. Intel oneAPI Math Kernel Library 2025.0 will require Intel(R) Advanced Vector Extensions (Intel(R) AVX) instructions.\n",
      "Intel MKL WARNING: Support of Intel(R) Streaming SIMD Extensions 4.2 (Intel(R) SSE4.2) enabled only processors has been deprecated. Intel oneAPI Math Kernel Library 2025.0 will require Intel(R) Advanced Vector Extensions (Intel(R) AVX) instructions.\n"
     ]
    }
   ],
   "source": [
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "from codes.model import Model\n",
    "from codes.solvers import solver, solverkvector\n",
    "from codes import kwant_examples\n",
    "from codes.kwant_helper import utils\n",
    "from codes.tb.transforms import tb2kfunc, tb2kfunc\n",
    "from codes.tb.tb import addTb\n",
    "from tqdm import tqdm\n",
    "import xarray as xr\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "id": "99f0e60c",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Intel MKL WARNING: Support of Intel(R) Streaming SIMD Extensions 4.2 (Intel(R) SSE4.2) enabled only processors has been deprecated. Intel oneAPI Math Kernel Library 2025.0 will require Intel(R) Advanced Vector Extensions (Intel(R) AVX) instructions.\n",
      "Intel MKL WARNING: Support of Intel(R) Streaming SIMD Extensions 4.2 (Intel(R) SSE4.2) enabled only processors has been deprecated. Intel oneAPI Math Kernel Library 2025.0 will require Intel(R) Advanced Vector Extensions (Intel(R) AVX) instructions.\n",
      "Intel MKL WARNING: Support of Intel(R) Streaming SIMD Extensions 4.2 (Intel(R) SSE4.2) enabled only processors has been deprecated. Intel oneAPI Math Kernel Library 2025.0 will require Intel(R) Advanced Vector Extensions (Intel(R) AVX) instructions.\n",
      "Intel MKL WARNING: Support of Intel(R) Streaming SIMD Extensions 4.2 (Intel(R) SSE4.2) enabled only processors has been deprecated. Intel oneAPI Math Kernel Library 2025.0 will require Intel(R) Advanced Vector Extensions (Intel(R) AVX) instructions.\n",
      "Intel MKL WARNING: Support of Intel(R) Streaming SIMD Extensions 4.2 (Intel(R) SSE4.2) enabled only processors has been deprecated. Intel oneAPI Math Kernel Library 2025.0 will require Intel(R) Advanced Vector Extensions (Intel(R) AVX) instructions.\n",
      "Intel MKL WARNING: Support of Intel(R) Streaming SIMD Extensions 4.2 (Intel(R) SSE4.2) enabled only processors has been deprecated. Intel oneAPI Math Kernel Library 2025.0 will require Intel(R) Advanced Vector Extensions (Intel(R) AVX) instructions.\n",
      "Intel MKL WARNING: Support of Intel(R) Streaming SIMD Extensions 4.2 (Intel(R) SSE4.2) enabled only processors has been deprecated. Intel oneAPI Math Kernel Library 2025.0 will require Intel(R) Advanced Vector Extensions (Intel(R) AVX) instructions.\n",
      "Intel MKL WARNING: Support of Intel(R) Streaming SIMD Extensions 4.2 (Intel(R) SSE4.2) enabled only processors has been deprecated. Intel oneAPI Math Kernel Library 2025.0 will require Intel(R) Advanced Vector Extensions (Intel(R) AVX) instructions.\n",
      "Intel MKL WARNING: Support of Intel(R) Streaming SIMD Extensions 4.2 (Intel(R) SSE4.2) enabled only processors has been deprecated. Intel oneAPI Math Kernel Library 2025.0 will require Intel(R) Advanced Vector Extensions (Intel(R) AVX) instructions.\n",
      "Intel MKL WARNING: Support of Intel(R) Streaming SIMD Extensions 4.2 (Intel(R) SSE4.2) enabled only processors has been deprecated. Intel oneAPI Math Kernel Library 2025.0 will require Intel(R) Advanced Vector Extensions (Intel(R) AVX) instructions.\n",
      "Intel MKL WARNING: Support of Intel(R) Streaming SIMD Extensions 4.2 (Intel(R) SSE4.2) enabled only processors has been deprecated. Intel oneAPI Math Kernel Library 2025.0 will require Intel(R) Advanced Vector Extensions (Intel(R) AVX) instructions.\n",
      "Intel MKL WARNING: Support of Intel(R) Streaming SIMD Extensions 4.2 (Intel(R) SSE4.2) enabled only processors has been deprecated. Intel oneAPI Math Kernel Library 2025.0 will require Intel(R) Advanced Vector Extensions (Intel(R) AVX) instructions.\n",
      "Intel MKL WARNING: Support of Intel(R) Streaming SIMD Extensions 4.2 (Intel(R) SSE4.2) enabled only processors has been deprecated. Intel oneAPI Math Kernel Library 2025.0 will require Intel(R) Advanced Vector Extensions (Intel(R) AVX) instructions.\n",
      "Intel MKL WARNING: Support of Intel(R) Streaming SIMD Extensions 4.2 (Intel(R) SSE4.2) enabled only processors has been deprecated. Intel oneAPI Math Kernel Library 2025.0 will require Intel(R) Advanced Vector Extensions (Intel(R) AVX) instructions.\n",
      "Intel MKL WARNING: Support of Intel(R) Streaming SIMD Extensions 4.2 (Intel(R) SSE4.2) enabled only processors has been deprecated. Intel oneAPI Math Kernel Library 2025.0 will require Intel(R) Advanced Vector Extensions (Intel(R) AVX) instructions.\n",
      "Intel MKL WARNING: Support of Intel(R) Streaming SIMD Extensions 4.2 (Intel(R) SSE4.2) enabled only processors has been deprecated. Intel oneAPI Math Kernel Library 2025.0 will require Intel(R) Advanced Vector Extensions (Intel(R) AVX) instructions.\n",
      "Intel MKL WARNING: Support of Intel(R) Streaming SIMD Extensions 4.2 (Intel(R) SSE4.2) enabled only processors has been deprecated. Intel oneAPI Math Kernel Library 2025.0 will require Intel(R) Advanced Vector Extensions (Intel(R) AVX) instructions.\n",
      "Intel MKL WARNING: Support of Intel(R) Streaming SIMD Extensions 4.2 (Intel(R) SSE4.2) enabled only processors has been deprecated. Intel oneAPI Math Kernel Library 2025.0 will require Intel(R) Advanced Vector Extensions (Intel(R) AVX) instructions.\n",
      "Intel MKL WARNING: Support of Intel(R) Streaming SIMD Extensions 4.2 (Intel(R) SSE4.2) enabled only processors has been deprecated. Intel oneAPI Math Kernel Library 2025.0 will require Intel(R) Advanced Vector Extensions (Intel(R) AVX) instructions.\n"
     ]
    }
   ],
   "source": [
    "# Create translationally-invariant `kwant.Builder`\n",
    "graphene_builder, int_builder = kwant_examples.graphene_extended_hubbard()\n",
    "h_0 = utils.builder2h_0(graphene_builder)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "id": "f4d1bb07",
   "metadata": {},
   "outputs": [],
   "source": [
    "def compute_phase_diagram(Us, Vs, int_builder, h_0): \n",
    "    gap = []\n",
    "    ks = np.linspace(-np.pi, np.pi, 300)\n",
    "    for U in tqdm(Us): \n",
    "        gap_U = []\n",
    "        guess=None\n",
    "        for V in Vs: \n",
    "            params = dict(U=U, V=V)\n",
    "            h_int = utils.builder2h_0(int_builder, params)\n",
    "            if guess==None:\n",
    "                guess = utils.generate_guess(frozenset(h_int), len(list(h_0.values())[0]))\n",
    "            model = Model(h_0, h_int, filling=2)\n",
    "\n",
    "            mf_sol = solverkvector(model, guess, nK=18)\n",
    "            hkfunc = tb2kfunc(addTb(h_0, mf_sol))\n",
    "            hkarray = np.array([hkfunc((kx, -kx)) for kx in ks])\n",
    "            vals = np.linalg.eigvalsh(hkarray)\n",
    "            gap_U.append(utils.calc_gap(vals, E_F=0))\n",
    "            guess = None\n",
    "        gap.append(gap_U)\n",
    "    return np.asarray(gap, dtype=float)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "id": "14f332f2",
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "100%|██████████| 10/10 [02:25<00:00, 14.56s/it]\n"
     ]
    }
   ],
   "source": [
    "Us = np.linspace(0, 3, 10, endpoint=True)\n",
    "Vs = np.linspace(0, 1.5, 10, endpoint=True)\n",
    "gap = compute_phase_diagram(Us, Vs, int_builder, h_0)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "id": "0d2ad9d8",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.collections.QuadMesh at 0x14c72ddd0>"
      ]
     },
     "execution_count": 9,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": "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",
      "text/plain": [
       "<Figure size 640x480 with 2 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "gap_da = xr.DataArray(data=gap, coords=dict(Us=Us, Vs=Vs))\n",
    "gap_da.plot(x=\"Us\", y=\"Vs\", vmin=0, vmax=1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "id": "a661ac28",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.collections.QuadMesh at 0x14e4c8ad0>"
      ]
     },
     "execution_count": 20,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": "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",
      "text/plain": [
       "<Figure size 640x480 with 2 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "np.log10(gap_da).plot(x=\"Us\", y=\"Vs\", vmin=-3, vmax=1) "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 37,
   "id": "18191ba0",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.02672641009348376"
      ]
     },
     "execution_count": 37,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": "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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "#Single shot calculation\n",
    "params = dict(U=0, V=1)\n",
    "filling = 2 \n",
    "\n",
    "h_int = utils.builder2h_0(int_builder, params)\n",
    "model = Model(h_0, h_int, filling)\n",
    "mf_guess = utils.generate_guess(frozenset(h_int), len(list(h_0.values())[0]))\n",
    "mf_sol = solver(model, mf_guess, nK=30)\n",
    "\n",
    "ks = np.linspace(-np.pi, np.pi, 200)\n",
    "hkfunc = tb2kfunc(addTb(h_0, mf_sol))\n",
    "hkarray = np.array([hkfunc((kx, -kx)) for kx in ks])\n",
    "vals = np.linalg.eigvalsh(hkarray)\n",
    "plt.plot(vals)\n",
    "utils.calc_gap(vals, E_F=0)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "e183c3cb",
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3 (ipykernel)",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.11.6"
  },
  "widgets": {
   "application/vnd.jupyter.widget-state+json": {
    "state": {},
    "version_major": 2,
    "version_minor": 0
   }
  }
 },
 "nbformat": 4,
 "nbformat_minor": 5
}