test_Kitaev.ipynb

{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 48,
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "import scipy.sparse as sp\n",
    "import scipy.sparse.linalg as sla\n",
    "import scipy.linalg as la\n",
    "import scipy.stats\n",
    "import numpy.matlib\n",
    "import matplotlib.pyplot as plt\n",
    "from  KitaevChain import *"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "plt.rcParams['text.usetex']=True\n",
    "plt.rcParams['font.family']='serif'\n",
    "plt.rcParams['font.size']=9\n",
    "plt.rcParams['axes.titlesize']=plt.rcParams['font.size']\n",
    "plt.rcParams['figure.figsize']=(6.8,4)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Benchmark"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Derivative of von Neumann entropy"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/home/jake/anaconda3/lib/python3.8/site-packages/scipy/sparse/_index.py:82: SparseEfficiencyWarning: Changing the sparsity structure of a csr_matrix is expensive. lil_matrix is more efficient.\n",
      "  self._set_intXint(row, col, x.flat[0])\n"
     ]
    }
   ],
   "source": [
    "mu_list=np.linspace(0,4,100)\n",
    "von_Neumann_entropy_mu_list=[]\n",
    "spectrum_gap_list=[]\n",
    "eigvallist=[]\n",
    "for mu in mu_list:\n",
    "    params=Params(mu=mu,Delta=0.1,L=400,bc=-1)\n",
    "    von_Neumann_entropy_mu_list.append(params.von_Neumann_entropy(np.arange(10)))\n",
    "    val=params.val\n",
    "    spectrum_gap_list.append(np.max(val[val<0])-np.min(val[val>0]))\n",
    "    eigvallist.append(val)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [],
   "source": [
    "derivative=(np.array(von_Neumann_entropy_mu_list[2:])-np.array(von_Neumann_entropy_mu_list[:-2]))/(mu_list[1]-mu_list[0])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": "<matplotlib.legend.Legend at 0x7f8dc5a0ad90>"
     },
     "execution_count": 14,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": "<Figure size 489.6x288 with 1 Axes>"
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig,ax=plt.subplots()\n",
    "\n",
    "ax.plot(mu_list,von_Neumann_entropy_mu_list,label='Entropy')\n",
    "ax.plot(mu_list,np.abs(spectrum_gap_list),label='Gap')\n",
    "ax.plot(mu_list[1:-1],np.abs(derivative),label='derivative Entropy')\n",
    "ax.legend()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": "(2.0, 2.2)"
     },
     "execution_count": 22,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": "<Figure size 489.6x288 with 1 Axes>"
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig,ax=plt.subplots()\n",
    "for index in range(eigvallist[0].shape[0]):\n",
    "    ax.plot(mu_list,np.array(eigvallist)[:,index],'k')\n",
    "    ax.set_ylim([-.3,.3])\n",
    "ax.set_xlim(2,2.2)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/home/jake/anaconda3/lib/python3.8/site-packages/scipy/sparse/_index.py:82: SparseEfficiencyWarning: Changing the sparsity structure of a csr_matrix is expensive. lil_matrix is more efficient.\n",
      "  self._set_intXint(row, col, x.flat[0])\n"
     ]
    }
   ],
   "source": [
    "Delta_list=np.linspace(0.1,2,20)\n",
    "von_Neumann_entropy_Delta_10_list=[]\n",
    "von_Neumann_entropy_Delta_30_list=[]\n",
    "von_Neumann_entropy_Delta_50_list=[]\n",
    "von_Neumann_entropy_Delta_70_list=[]\n",
    "\n",
    "for Delta in Delta_list:\n",
    "    params=Params(mu=0,Delta=Delta,L=400)\n",
    "    von_Neumann_entropy_Delta_10_list.append(params.von_Neumann_entropy(np.arange(10)))\n",
    "    von_Neumann_entropy_Delta_30_list.append(params.von_Neumann_entropy(np.arange(30)))\n",
    "    von_Neumann_entropy_Delta_50_list.append(params.von_Neumann_entropy(np.arange(50)))\n",
    "    von_Neumann_entropy_Delta_70_list.append(params.von_Neumann_entropy(np.arange(70)))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": "<matplotlib.lines.Line2D at 0x7f8dc6372130>"
     },
     "execution_count": 16,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": "<Figure size 489.6x288 with 1 Axes>"
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig,ax=plt.subplots(figsize=(6.8,4))\n",
    "ax.plot(Delta_list,von_Neumann_entropy_Delta_10_list,'.-',label=r'$|A|=10$',lw=1,)\n",
    "# ax.plot(Delta_list,von_Neumann_entropy_Delta_30_list,label=r'$|A|=30$',lw=1)\n",
    "ax.plot(Delta_list,von_Neumann_entropy_Delta_50_list,'.-',label=r'$|A|=50$',lw=1)\n",
    "ax.plot(Delta_list,von_Neumann_entropy_Delta_70_list,'.-',label=r'$|A|=70$',lw=1)\n",
    "ax.legend()\n",
    "ax.set_xlabel(r'$\\Delta$')\n",
    "ax.set_ylabel(r'$S_A$')\n",
    "ax.text(-.01,np.log(2),r'$\\log(2)$',ha='right',va='center')\n",
    "ax.set_yticks(np.arange(.8,1.3,0.1))\n",
    "ax.axhline(y=np.log(2),ls='--')\n",
    "# fig.savefig('/mnt/d/kitp/Rp_SPT/2/entropy_vs_Delta.pdf',bbox_inches='tight')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## von Neumann Entropy"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {},
   "outputs": [],
   "source": [
    "def generate_A_dep(mu,von_Neumann_entropy_list):\n",
    "    subregion_max_list=np.arange(2,40)\n",
    "    von_Neumann_entropy_list[mu]=[]\n",
    "    params=Params(mu=mu,Delta=1,L=400)\n",
    "    for subregion_max in subregion_max_list:\n",
    "        von_Neumann_entropy_list[mu].append(params.von_Neumann_entropy(np.arange(subregion_max)))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/home/jake/anaconda3/lib/python3.8/site-packages/scipy/sparse/_index.py:82: SparseEfficiencyWarning: Changing the sparsity structure of a csr_matrix is expensive. lil_matrix is more efficient.\n",
      "  self._set_intXint(row, col, x.flat[0])\n"
     ]
    }
   ],
   "source": [
    "von_Neumann_entropy_list={}\n",
    "for i in (0,2,3,10):\n",
    "    generate_A_dep(i,von_Neumann_entropy_list)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAekAAAEaCAYAAAA1yK8gAAAAOXRFWHRTb2Z0d2FyZQBNYXRwbG90bGliIHZlcnNpb24zLjMuMiwgaHR0cHM6Ly9tYXRwbG90bGliLm9yZy8vihELAAAACXBIWXMAAAsTAAALEwEAmpwYAAAczElEQVR4nO3de3Bc53nf8d8jijBpicKGF1sXlKJWtlU5U8kGl4pAyyocLH2VU48LkUltOUltQ7FTp2ntkKPWTN1qWpZoO27jtgnXadPWdsYikbRTJ1MnXGZQxeXGIgBZ0viiqlxdAl0p0ktdLGpB4OkfexZZAIvLAnt5d8/3M8NZ7p5nXz1nD8Qf3nPOnmPuLgAAEJ5LWt0AAACojpAGACBQhDQAAIEipAEACBQhDQBAoC5tdQO12Lp1q+/YsaPVbQAAUDfj4+Mvuvu2asvaKqR37NihsbGxVrcBAEDdmNmTiy1jdzcAAIEipAEACBQhDQBAoAhpAAACRUgDABAoQhoAgEAR0gAABIqQBgCgRXI5SbrmysWWE9IAACwil5MOHSqHaX3rczlpYECSrrxmsZq2uuIYAABrlctJo6NSf7/U17d03cCAVCxKXV3SiRP1rR8dLdUuhZk0ACAozZi9HjxYelzqPeUQnZ4uPY6OLj12rfX9/aUwl9wXq2nKTNrM0pL2uPuBRZYPScpLSrj7SDN6AgA0x0pnruXaZsxeK4N0sfpyiJbH7u9fuvda6/v6Sv3u3v38M4vVNCWk3T1rZndXW2Zm+yVl3X3CzI5IIqQBoIlqCdFa6xsZoqupryVIyyG60nWttb78Hunp5xZbHsIx6V2qCGYz63X3iYrnQ5KGJGn79u3N7w4A2ky7zlyl5s1eawnelYTtauuXE0JIz1eofOLuGUkZSUqlUovutweAThWXmavUvNlrPYO0kUII6VOSEuUn7p5vXSsA0ByNOsO43Weu5fe0cvYakmaeOJas3JVtZkMVs+S9ZiZJx5vRDwDUW6Nmu8xc461pJ45J2jnvtUz0WFC0O1vShAAgAKHsYmbmGm8h7O4GgIYLJXSlxp5hXH4PIdoZCGkAbaldQ1dq/BnG6ByENIAgxCl0y+8heLEcQhpAQxC6wNoR0gDqjtAF6oOQBrAitcyMCV2gPghpIMYadUENQheoD0IaiKlGXlCD0AXqg5AGOkijdknXOjOWCF2gHghpIGCNPEO60RfUALB2hDQQqEafIc0FNYDwEdJAE4V0hrRE8AKhI6SBJgnxDGkAYSOkgTVo5MyYM6QBENLAKjV6ZiwRukDcXdLqBoCQ5HLSoUOlx+VUmxkvpTwzvvfe5QMdACRm0sAsZsYAQsNMGh2NmTGAdsZMGh2LmTGAdsdMGm2FmTGAOGEmjbbBzBhA3BDSaBvN+J4xAISEkEbLrfSCIMyMAcQNIY2WqmUXNjNjAHFDSKOlVrMLm3AGEBec3Y26q+UM7PIu7HXrVr4LGwDigpk06qrWM7DZhQ0AiyOkUVe17r6W2IUNAIthdzeWxe5rAGgNZtJYEruvAaB1CGksid3XANA67O6OIXZfA0B7YCYdM+y+BoD2QUjHDLuvAaB9sLs7Zth9DQDtg5l0B1jpDSokdl8DQDshpNtcrceYJXZfA0C7YHd3m6t2jBkA0BmaMpM2syFJeUkJdx+psjwt6ZykZLXlWNxq7rEMAGgPDZ9Jm9l+SWPunpW0p8rytErhPSEp2eh+Ok35GPO9965sVzcAoH00Yya9S9Ls7NjMeqNAliS5e9bMxs1sn6RD898czcKHJGn79u1NaLf1ajkRTOIYMwB0qlacOFaofGJmSUkHVJpFH9a82ba7ZyRlJCmVSnlzWmyd1ZwIBgDoTM04ceyUpET5ibvn5y0fdPdsFMbHotCOLU4EAwCUNSOkM5JSZtYr6Xj5xWg3tiSNmNlgtPxclRCPFS42AgAoM/f22YOcSqV8bGys1W00XK3HpAEA7cvMxt09VW0ZFzNpAk4EAwCsBiHdYJwIBgBYLa441mCcCAYAWC1CusE4EQwAsFrs7m4w7joFAFgtQroJOBEMALAa7O5ehVxOOnSo9AgAQKMwk64RZ2sDAJqFmXSNOFsbANAshHSNOFsbANAs7O6uEWdrAwCahZBeBc7WBgA0w5K7u80sbWZHah3UzAaXWJaM++0oAQBYiSVD2t2zkjbXMqCZpSVNRH9PmFlvdCvK/dGYeUnpVfYLAEBsNOLEsT0V94TeK6ng7iOS9plZInp9LArzYPDdZwBAaFZ8TDoK2L2S8pKS7p6JdltXhu2YpET5ibtnKsdw90L0OGFmhyVlV9t4PfHdZwBAiGqZSR+WdDTaBX69mfVKKh9bPqdSeOclFea/MdrVfee8lxO1Nvvcc88pt8Kpbi6X06FDh1ZUPzoqvf66a3q69Ljcd59rGZv6+taH1Evc6kPqJW71IfUSt/pm9CLpysWWm7svOYCZHXP3O83smKRPu3shmgXfF5UUJJ0rz5LN7Ii7313x/rRK4a2K3eAys8PufmBFaxFZv6XHt33g13TzzTfriiuukCTdcdNVuqtvh14rTuuXfu8BSdJLL72khx56SO4zev1H9+uP//1B3XDTTn3m6+MLxvz4rdfq2e+e1We/cI223vEjSa63ve01XXXVZZKkT787qfTb36zTZ17RP/rDR+aMbXaJvnTnrRr6W7fr+8+c1z/71g8WjP/Bnil95s73S1uTStz+iTm9S9Jvfvjt+umru/Wdx17UV/7ssQXjf+UTu/W333ubsj94Xl/98/yC8e9667T23vFerbvuFm165wcXjP/bH9+pzZd16djYX2pkfHLB+L9/923qf/dufS33hP7o4WcXjP/rN0kDAwPquumDeuNbbpkz/ob16/Rf/+4tkqTfOvGY/s//e3HO+P76q/rvn/+g+vr6dPjbP9LEkz+eM/ZV3Ru079oLGhgY0MZ33aU3vPn6OeMnt12mQx+9SZJ0zx8+rO+dfnZO7z93e69+Z6i0I+fXv/mgnj1/Yc74b770J/rdz31YxWJRWz9yj975M7fN+Wze9Zat+rWBt0qSfvE/P6AXzv54zvi//L6U/vldPytJ2ndk4f9wb990QYc/9SFNzUjbBr+04LMf3NmjO1N/TedeLeozXx9f8Nl/4SO36B8O9uuZwmv6B/d9b8H4735TUfs/9gHNXLZNm9/3qwvG/9zPvlW3vXXr7M/e/PEP/cKt+sUP3a7xJ89p+NuPLhj/I9de1Cc/+j7ZlTeqe/e+BeP/i4/+DV2/7XJlf/C8/s0ff2/O2DfffLP+06dv19WJjfrWQ8/o63/x5JyxX3rpJd1/6BN6/aWzuuLm9+pnfv7vzxlbkv7LL9+ijV3r9LXcE/r97zy6YPz/9RvvkyRl7j+tEz98Yc57L7z6so5/8SMqFotKvOsXtOuOj88Z/6fe2KXfuWunJOnwt3+k0UeenDP+e259p77x9/ZIkv7pt76vHzzz0pzxL5t5Vd/8/M+pWCxqy/s/p96/+f4547/96iv0Tz7805JKP3uP/uULc8YffM9O/dYnByRJv/K1cf34J8U5429/w2v6D5+9Q8ViUdsGv6R37Nw1Z/yBG9+koduvlyR94F/9yYLP5u/cdsOCf/cqP/vvfvPf6aWH/lRvuGKLbr/nvy347D9+67X68M1X65nCa/rkV+9fMP7nP/SOOf/uzR//5O/+pl49Pa43Xv02vetzX14w/v7336Cd127W+JPn9MWjpxaM/68/duucf/fmj/+dL/+qXnvhCV1+Q5/6fumLC8b/8r53zP7s/cc/fWTB+N/47Hvm/Ls3f/z/fe8+FX/yirp33qFbBj+zYPz77i7tSv3HX/sz/d6fjM0Z+01bfmrBv3uVYz/43e/oxf9xSF1dXfrUV76l5y++cc7YV3Vv0L/9+XdKkn4lk9X/vH9Cz37jgNzdVMVyZ3f3SkpGu7oPSNobhe5pd59QKaAPS7qn4ozuQsX709HyI5KOVbyelHRqqf/2YtxnVCgUlqwpFAqlkHDp4sWLGl1manz27B/pkks+JukJSQ9paursisZ2n9FDDz+05NgTEw+qWCxqZma65t7dZ/TAAw8sWZ/L/UU0/syqxr//z+9fsn50dFTFYjF6T23jz8zMLPvZ/9X4vuz483ufnJxctFaSnnrqKRWLRU1PT2tmpvbP5vTp00vWP/Z/H4vGX91n//3vL/ylrtIjjzxSGn+VPzsTEw8uWT82Nrbin835Y6+kl6mp0md/8eLFmntfrv7cubOz23Z6errm8Z9//vkl65955pk1jf/UU08tWf/444/Pjt+Iz/7ixYuanp7W1FSx7p99oVDQxany+FMNGX9qaqr0szNV/5+dQqGgqeizv7jMtj19+nTNY8/MzGh6elrFYnHZn4PJyUm5zyxZE/3juLo/kvZLSkR/H1Jp9/fQCt63bM0i7/ONGzf6yZMnfSknT570jRs3+rp16+pe38ixqeezD7U+pF7iVh9SL3Grb1YvkmZ8kdxbdnf3UqLZc0GlY9IplY5ZF8xs0EtndFd7T0JSykvHtmvS09Pjx44dU98KzurK5XIaHR1Vf39/3esbOTb1fPah1ofUS9zqQ+olbvXN6GX37t1Pu3tPteVrCulmS6VSPjY21uo2AACoGzMbd/dUtWXcYAMAgEAR0gAABIqQBgAgUB0b0lzmEwDQ7jryVpVc5hMA0Ak6MqRHR0sBPT1dehwdJaQBIFRTU1OanJzUhQsXli9ucxs2bFBPT4/Wr1+/ovqODOn+/tIMujyT7u9vdUcAgMVMTk5q06ZN2rFjh8yqXh2zI7i7zp49q8nJSV133XUrek9HhnRfX2kX9+hoKaCZRQNAuC5cuNDxAS1JZqYtW7bozJkzK35PR4a0VApmwhkA2kOnB3RZrevZsWd3AwDQ7ghpAAAC1bG7uwEAnanWm1g0WiaTUTKZVKFQ0ODg4PJvqAEzaQBA28jlchoYGNDBgwc1MDCgXIuvWDU8PKxUKqV0Oq3jx4/XfXxCGgDQNkZHR1UsFjU9Pa1isajR0dFVj5XJZJTP5yWVwrZSPp/XyMjIgj/l+rJTp04pkUjMPp+YmFh1P9WwuxsA0Db6+/vV1dWlYrGorq4u9a/hQhjj4+MaGhpaELySlEwmlUwmax6zMrDroSkhbWZDkvKSEu4+UmX5oKSCpF53H56/HAAASerr69OJEyfqekw6m80qnU6rUCjMhmw+n686K+7t7Z0T3rt27VKhUJh9vppgX0rDQ9rM9kvKuvuEmR2RNDJveVrSZncfMbOFv84AAFChr69vzeGcz+eVz+eVzWZ1+vRpSaUALlvpTHpoaEhHjx6VJO3Zs2dNPVXTjJn0LlUEs5n1unvlryd7JJ2OwjopKVP55mgWPiRJicRfVy7HRUoAAGuTzWZ15MgRJZNJpdPpVY+TSCQ0NDQkaW7I10srThwrzHuekJR396ykPWaWqFzo7hl3T7l7qlC4TAMD3H4SALA2p0+frvuu6UZoRkifUimIJUnuPn+X9ngtg5XvagUAwGodPny41S2sSDNCOiMpZWa9kma/RBbtxpa7ZyT1Rru7j7t7YanBuKsVACAuGn5MOgrd8nHmiYrXMxV/X9EZ3ddcIx07xjFpAEA8tNXFTK68koAGAMRHW4U0AABxwhXHAABtJZcrnUDc39/6vauFQmH2O9f5fF779++v6/jMpAEAbSOXkwYGpIMHFcRXco8ePapEIqHBwUHdd999c64+Vg/MpAEAbWN0tPRV3Onpv/pK7mpn05lMRul0WslkUsPDw3NmwSu9LGj5QiZlbXntbgAA6qG/v/RV3GJx7V/JrecNNoaHh3Xs2LHVN7MIQhoA0Db6+qQTJ+p7THotN9gov39wcHDtjVSx5pA2s3dIul7SXnfft+aOAABYQl/f2sO5XjfYyGazOnDggDZv3qxz585pfLymi2gua00hbWZHJT0QPf2Xa28HAIDGq9cNNtLpdN2DudKazu52972SHpRk7v5gfVoCAKCxYnODDXc/ISljZl+oQz8AADRcrG6w4e7nJf1BPcYCAAAlNYW0mf2GmX3KzK6Yv8zdH69fWwAAoNYTx/Lu/geSZGa/LSkpKS/psLs/UefeAACItVpD+seSZGbdKn3lakv0/KOSnqhvawAAxFutIW1m9mlJOyVVXlrlfP1aAgAAUo0h7e4nzCyv0m7vE9GMOimpuyHdAQAw3/lXpPMvS92bpO7LW92Nstns7I016n3lsZovZhKdIPZ49PfzZiZJVteuAACo5vwr0sOPSjMuXWLSTTe0NKgnJiZUKBQ0ODionTt3tj6k54suYsKFTAAAjXf+5VJAS6XH8y+vOqTrcRes8vNMJqN77rlnVX0shRtsAADaR/em0gy6PJPu3rTqoep1F6xEIqF0Oq0DBw6EN5MGAKBpui8v7eKu4zHptdwFa3h4WIODg0omk8rn83PGqAdCGgDQXrovX3M41+suWIODgyoUChoZGdG+ffvqGtASIQ0AiKF63QWrHOSVAV9Pdbl2NwAA7SQ2d8ECAKDdxOouWAAAoP4IaQAAAkVIAwAQKEIaAIBAEdIAgPaSy0mHDpUeA5DNZnXgwIE5r2UyGWWzWY2MjKxpbEIaANA+cjlpYEA6eLD0GEBQp9PpOZcWHR4eViqVUjqd1vHjx9c0NiENAGgfo6NSsShNT5ceR0dXPVQmk5kN1+Hh4TnL8vm8RkZGFvypdp3v+U6dOjXnymPVLi+6UlxxDADQPvr7pa6uUkB3dZWer1K9brCxnLVcKpSQBgC0j74+6cSJ0gy6v7/0fI3WcoONanbt2qVCoTD7fC1hT0gDANpLX9+aw7leN9iQSiFfDvXe3l4NDQ3p6NGjkqQ9e/asqU9z9zUN0EypVMrHxsZa3QYAoI5++MMf6sYbb2zqfzOTySidTrfk+t3z19fMxt09Va2WE8cAALHDDTYAAAgUN9ioYGZDZpY2s8ElanqXWg4A6FztdOh1LWpdz4aHtJntlzTm7llJSx1BT0va3Oh+AABh2bBhg86ePdvxQe3uOnv2rDZs2LDi9zTj7O5dkmavi2Zmve4+57x2M0tLykpacODczIYkDUnS9u3bG9spAKDpenp6NDk5qTNnzrS6lYbbsGGDenp6Vlzfiq9gFSqfRKGdNbPeasXunpGUkUpndze+PQBAM61fv17XXXddq9sIUjNC+pSkRPmJuy+4tEs0k+6VdL2ZJdy90IS+AAAIWjNOHMtISkUz5dkrjUe7seXuE9Hx6i1N6AUAgLbR8Jl0NCvORE8nKl7PzKube58vAABiju9JAwAQKEIaAIBAEdIAAASKkAYAIFCENAAAgSKkAQAIFCENAECgCGkAAAJFSAMAEChCGgCAQBHSAAAEipAGACBQhDQAAIEipEN0/hXpqWdLj9SH20vc6kPqJW71IfUSt/om9HLN1m1XLra44beqbBvnX5HOvyx1b5K6L69f7WrGfvhRacalS0y66Yal3xOn+pB6iVt9SL3ErT6kXuJW36Rerty85ZrFSjp3Jl3rb0oPPyo9/nTpcan31FK7qvqXSxtYKj2ef5n6EHuJW31IvcStPqRe4lbftF5s0ZLODOlGBmOjN1r3ptJvYFLpsXsT9SH2Erf6kHqJW31IvcStvkm9uNwXKzFffFlwUqmUj42NLV/41LOlgC677hpp+1WL14e0+6P8nkbtTm/3+pB6iVt9SL3ErT6kXuJW34Reet6SfHryzAs91RZ3Zkg3OhgbvdEAALFhZuPunqq2rL1OHCtOlQJvuaDrvrwUzLUEY/flKw/QWmpXUw8AgNrtmPTrUys7xiyVQnH7VYQjAKBttVdISys7+QoAgA7QfiG9kjPmAADoAO0V0m9Yv7KTwAAA6ADtFdJd6wloAEBstFdIAwAQI4Q0AACBIqQBAAgUIQ0AQKAIaQAAAkVIAwAQKEIaAIBAEdIAAASKkAYAIFCENAAAgSKkAQAIFCENAECgLm3Gf8TMhiTlJSXcfWTesoSkZPmPuw83oycAAELX8Jm0me2XNObuWUl7qpTslVSIwntfFNoAAMReM3Z375JUKD8xs97Khe6ecfd8xfNC5XIzGzKzMTMbO3PmTINbBQAgHK04Jl2o9mI0475z/utRiKfcPbVt27ZG9wYAQDCaEdKnJCXKTypnzWVmlpY0Mv91AADirBknjmUk7TUzSTpeftHMhtw9EwX0YUnnJG2WtLMJPQEAELyGh3R0jDkTPZ2oeD0TPWZFMAMAsADfkwYAIFCENAAAgSKkAQAIFCENAECgCGkAAAJFSAMAEChCGgCAQBHSAAAEipAGACBQhDQAAIEipAEACBQhDQBAoAhpAAACRUgDABAoQhoAgEAR0gAABIqQBgAgUIQ0AACBIqQBAAgUIQ0AQKAIaQAAAkVIAwAQKEIaAIBAEdIAAASKkAYAIFCENAAAgSKkAQAIFCENAECgCGkAAAJFSAMAEKj2CunnnpNyuZXV5nLSoUONqW/k2NS3Ty9xqw+pl7jVh9RL3Oqb0Ms10pWLLnf3tvmzU3LfuNH95Elf0smTpbp16+pf38ixqeezD7U+pF7iVh9SL3Grb1IvOyX3RXKvvWbSklQsSqOjS9eMjpbqpqfrX9/Isannsw+1PqRe4lYfUi9xq29WL0tov5Du6pL6+5eu6e8v1a1bV//6Ro5NPZ99qPUh9RK3+pB6iVt9k3pxyRcrMfdFlwUn1dPjY8eOSX19yxfncqXfUvr761/fyLGpb59e4lYfUi9xqw+pl7jVN6GXnt27n55076m2uL1COpXysbGxVrcBAEDdmNm4u6eqLWu/3d0AAMQEIQ0AQKAubcZ/xMyGJOUlJdx9pNblAADEUcNn0ma2X9KYu2cl7al1OQAAcdWM3d27JBXKT8yst5blZjZkZmNmNnbmzJkGtgkAQFhacUy6UMtyd8+4e8rdU9u2bWtYUwAAhKYZIX1KUqL8xN3zNS4HACCWGv49aTNLSNoraUxSsnximJkNuXtmseWLjHVG0pMNbXjltkp6sdVNNFGc1jdO6yrFa31Z187Vzut7rbtX3VXcVhczCYmZjS325fNOFKf1jdO6SvFaX9a1c3Xq+vI9aQAAAkVIAwAQKEJ69TKtbqDJ4rS+cVpXKV7ry7p2ro5cX45JAwAQKGbSAAAEipBeBTNLVj6iM7GdOxPbtXN14rYlpGsUfa/7iJkdaXUvjWRmaTM7PO+1oej1wVb11Sjz17dTt7OZJcys18wGo+vml1/vuG1bbV07dbuWlbdh5XbsxG0rLVzXTt22HJOuUfSDkHT3iVb30mhmdszd74z+vl9S1t0nzOyIu9/d4vbqbt76JtSB2zm641zW3fNmNi5pQFL5tY7atousq9SB21Wave9B0t1HzGzc3Xd26v+3i6xrQh24bZlJr04q+i1uqNWNNNFyN0rpRB23naNr4ecrnhfUodt2kXWVOnC7SlIUTtlovQ5FL3fqtq22rlIHbltCukbuXoj+589KurPV/bRQodUNNFKnb+dohrXYehWa2ErDVa5rp2/X6BeRrKR9i5QUmtZMg81f107dtoR0jaLjO4lW99ECsboRSidvZzNLS6q8Rn7Hbtv569rh23W/mSWj7ZeM1rMjt221de3UbXtpqxtoQ0dV+qHYLOlYq5tplOgft6SZ9Ua7ljKS9pqZJB1vaXMNUGV9O3I7R+t5WNI5SZsl7VSHbttF1rUjt2tkRFIiOpHqPncvmFlHbltVX9eO3LacOAYAQKDY3Q0AQKAIaQAAAkVIAwAQKEIaAIBAEdJAzK30cpGddllJoB0Q0gA2V3vRzA5HX2Nasg5A4xDSABaouItQx9xNCGhHhDSAapIqXfwi0eI+gFgjpAHMUXHsOSnp+lb2AsQdlwUFMCu69vFEdHvHhDroRgVAO2ImDUDS7G0Mv1pxE4akStdC5rg00CLMpAFImr1H753znrO7G2ghZtIAAASKu2ABABAoZtIAAASKkAYAIFCENAAAgSKkAQAIFCENAECgCGkAAAL1/wGs8w84owGnGQAAAABJRU5ErkJggg==\n",
      "text/plain": "<Figure size 489.6x288 with 1 Axes>"
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig,ax=plt.subplots(figsize=(6.8,4))\n",
    "subregion_max_list=np.arange(2,40)\n",
    "for i,color in zip((0,2,3,10),('k','b','pink','red')):\n",
    "    ax.plot(subregion_max_list,von_Neumann_entropy_list[i],'.',label=r'$\\mu={}$'.format((i)),color=color)\n",
    "ax.legend()\n",
    "# ax.plot(subregion_max_list,1/3*np.log(subregion_max_list))\n",
    "ax.margins(x=0)\n",
    "ax.axhline(y=np.log(2),ls='--')\n",
    "ax.text(-1,np.log(2),r'$\\log(2)$')\n",
    "ax.set_xlabel(r'$|A|$')\n",
    "ax.set_ylabel(r'$S_A$')\n",
    "\n",
    "fig.tight_layout()\n",
    "fig.savefig('/mnt/d/kitp/Rp_SPT/2/SA_vs_A_L_fixed.pdf',bbox_inches='tight')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": "[<matplotlib.lines.Line2D at 0x7f8dc499cb80>]"
     },
     "execution_count": 21,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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yQBMfspW6+EQk52zd6qaJDxvm1s+7/HJYssRtHrhgxc7deKCuvFykFpSI5Axr4a9/dcsTLV4M3/0uTJsGxxzjrrfWjQeoKy8HKaBEJCd88AFceSXMnQtHHeXWz/ve95rf01Y3HqgrL9eoi09EstoXX7ip4scfD6EQ/M//wIIFMOgYzcjLd2pBiUhW+uoruP9+tyfTxo3wi1+4CRFFRZqRVygUUCKSVayF559340xLl7puvGnT4Oijd9yjGXmFQV18IpI1FiwAvx/OOcctSfTyy26sKTGcQF15hUIBJSIZ98UXMHYs/Nu/wd//Dg884FaBGHh08injsa68q759ZLOZepJf1MUnIhnz1Vdu0sNtt8HmzfDf/w033QT9+rU9ZRzUlVcI1IISkS5nLTz7rHt+afx4OPVU+Mc/3MO3/aKZk2ycSQqLAkpEutT8+XDGGXDuuUCP7VxR8Rm3PNjAkUc2v0/jTGKstan9hsaUA2HAY62tbHHNA5QDoWTXE5WUlNiampqU1iYimbNqFUyaBI8+6qaKXzZuI3/e/BbbmrYn7cKDnTcSlPxjjKm11pYku5bSFpQxZjxQY60NAqVJbpkIhKLXx6TytUUkO23ZAhUVcPjh8MQTbjWIJUvg4JNXsq1pe5tdeMWD+3HFGcMUTgUq1V18I4BI7MAY42vjXo8xxpt4whhTboypMcbUrF69OsWliUhXshZmz3bjTNdd57r1Fi50zzR5POrCk/alexZfpMXxZKDcGFMPFLW82VobAALguvjSXJuIpEko5FpKb74JBxz2FQ88tZUrfrJPs3u06oO0J9UBVQ14YgfW2nDiRWttxBgTiP4ebnldRHLbypVunOnxx2Hffk3s970P2eO4T7j/Y8PIup3HmDRVXNqS6i6+AFAS7dqrip2MTpwg2qU32hhThmtNiUge2LIFJk92u9k+9ZRbpuj6J5ax9/A6rLGaJi67JKUtKGtthGgXHW6mXux8IPp7OOG6iOQ4a6GyEq69Furq3BJFU6e6jQRr6/rx6Hvd2NbYpDEm2SVaSUJEdkltLYwbB2+/DV//utun6Vvf2nFdY0yyuxRQItIpK1bADTe4KeP9+jdxwVVrGHdFT77h3TmANMYku0MrSYhIh2zeDHfc4caZ/vhHuHDsFvpfPJd5vaq58PF5Oy3oKrK7FFAi0iZrYcYMt836pEnwne/Ahx/CN8Z8yvYeW7VWnqSNAkpEWlVTA6ecAuef7xZxfe019/Dt0KF60FbST2NQIrKTFSvg+uvhySdh0CB45BG46CLo3n3HPZoEIemmgBKRuM2b3VJEd9xpaWyEi/5rC/fdtRd9+ya/X5MgJJ0UUCISH2caPx6WL4c+R3/OgNM+4t3+X7G4YSTFfRVC0vU0BiVS4N57D04+GS64AAYMgHH3fMrAs0N033ezJj9IRimgRArUp5/ChRfCCSdAOOz2aaquhp/8R29NfpCsoC4+kQKzaZNbjmjKFNi+HSZOdL/2iS42rskPki0UUCIFoqkJ7rx/I9Pu6EVkdU9GjXIbCR522M73avKDZAN18YkUgHnzYHhxIzeO682mbps45MJ5TJjakDScRLKFAkokjy1fDj/+MZx4InzyCQz49/fZ/6dv0/PAtZr8IFlPASWShzZuhJtvhiOPdCs/3HAD/PWtDfT3raBHN01+kNygMSiRPNLUBE8/Dddd51aDGDPGjTMNHgygyQ+SWxRQInninXfc/kzV1VBSAjNnuuebEmnyg+QSdfGJ5LgX34lQ8q0NnHyye7bpySfhb3/bOZxEco1aUCI56ssvYdz1m3nsd+4Bpv7fXMKM6f055Ri1kCQ/KKBEckxTEzz1lHu4duXKveh9zGd4TlvEHvtuYcGqIxVQkjfUxSeSQ95+G77xDbf1xSGHwKOz13PwuQvYY98tmpkneUctKJEcsGwZTJjgJj4cdJBrQf3oR9CtW1+GF2tmnuSnTgWUMeZ4YCgw2lo7Ji0ViUjchg1w111uj6Zu3dyzTddeC71777hHM/MkX3U4oIwxM4H3ood3paccEQE3zvTkk25X288/d6tBTJ7suvVECkWHx6CstaOB+YCx1s5PX0kihe3hmRsYctQWLrnEPWD77rvwhz8onKTwdGqShLV2LhAwxlyTpnpECta//gX+s7ZSPmYfVnxuOeCcv/PAMw2MHJnpykQyo9OTJKy164wxs9NRjEgh2rAB7rwT7r4b6NYDzzc/Zp9vhOnZq4m//asPJUM0viSFqdUWlDHmWmPMpcaYvi2vWWv/ld6yRPLf9u1uF9vDD3cTIc4/H557fT37ne7CSdPGpdC11YIKW2tnAxhjfgd4gTBQYa1d1gW1ieStN96AK6+E+fPhpJPg+efd803gYdD+mjYuAm0HVAOAMWZf3LTy/tHjc4Fl6S9NJP+EwzB+vNsC49BD4ZlnYPRoMGbHPZo2LuK0FVDGGHMZUAzMSji/Lr0lieSf9evdONM990CPHnDbbXD11bDXXpmuTCR7tRpQ1tq5xpgwrqtvbrQl5QX27bLqRHJYbV0D7yxeyxe1BxC4uzdffAE//akLqgMPzHR1ItmvzVl80ckQ/4r+eZ1x/RCmra8RERdO/zHpn6yacxRbv+jN8JJGXnyxByUlma5MJHd0app59AFdPaQr0oalS+FnF/Vk+dsn0L3vJgadHeLS/+5LScmwTJcmklO0WKxIiqxbB3fcAffdB9179GbA6R/TpzjMHnvBiUMPy3R5Ijkn5QFljCnHTUf3WGsrk1z3A/WAN9l1kVwTe55p0iRYswYuvhhuv92wYusg5oW7a7q4yC5KaUAZY8YDQWttyBgzHahscd2PC65g9M8iOe3VV93zTAsWwCmnwL33gs/nrh2ApouL7I5Ub1g4AojEDowxvsSL1togMNEYMwsItvxiY0y5MabGGFOzevXqFJcmkjqLF8M558CZZ7op5LNmuYdvfb52v1REOijdO+pGEg+MMV5gAlAFVLS82VobsNaWWGtLBg4cmObSRDovEoFrroFjj4W5c90WGB99BGVlzR+2FZHdl+oxqGrAEzuw1oZbXC+z1k4BMMZgjPEmuUck6zQ2wiOPwI03wtq1cMklcPvtsP/+ma5MJH+lugUVAEqiXXtVsZPRiRMAlcaYsuj1eoWTZLvaugZ++ZvPOOpr2/mv/3Itp9paF1YKJ5H0SmkLylobwYUUQCjhfCD6exg3w6/ZdZFs9OfX1nHh2K1sXHwQPT2bmPJQE9eU91FXnkgXSfcYlEjOaWiAq66CUaV92VRXhOe0jzj40jfY+4jPFU4iXUgP6opENTZCIAA33QT19XDO+VtZsN/b2D23aG8mkQxQQIkAc+a455k+/BBOP909zzR8+B7U1vm0N5NIhiigpKAtWuSmjb/4IgwdCs8+C2efvWPKuPZmEskcjUFJQaqvh3Hj4Ljj4K23YOpUWLjQPXyrcSaR7KAWlBSUbdtg+nS4+Wb30O1ll8Gtt8KgQZmuTERaUgtKCsb//i8MHw6//CUcfzzMnw8PPaRwEslWCijJex99BP/+7/C977kW1F/+AsEgfP3rma5MRNqiLj7JS7V1DQTnNzD/LwdS+dSe9OkD06bBL34BvXplujoR6QgFlOSdvy1p4IdXrGTNm8No+qonZT/ewm/v3hOtPyySW9TFJ3nDWjdd/Oxv9eaLOcfQa791HHzJm5x+yacKJ5EcpBaU5IWFC93yRHPmwKGHdeegMTX0GrKKXj21AoRIrlJASU5bs8ZNGZ8+HfbZB+65By6/vDsfrBzKvLBHK0CI5DAFlOSkrVvht7+FW26BDRvg5z+HX/8aBgxw17UChEjuU0BJTomNM119Nfzzn/Dtb8Pdd7t9mkQkv2iShOSMf/wDvvMd+MEP3HJEL77oHr5VOInkJwWUZL3Vq+Hyy90qEDU1cN998MEH7uFbrZsnkr/UxSdZa+tWeOABt1bel1/CFVe4CRH9NSlPpCAooCTrWAsvvODGmZYscUsUTZsGRx+d6cpEpCupi0+yygcfQGmp25OpZ0946SX3S+EkUnjUgpKMq61roKo2QvXsA3numT3weOD++2HsWBdSIlKYFFCSUe/+s4GzL1/FmreHYrd154KfbuGB3+xJUVGmKxORTFMXn2SEtfDcc/DDM3qzeu5R7HlwPQf/7E1O/s9PFU4iAqgFJRnw/vtw5ZXw2mvgPbw7e15QTa/BX9Czh9bNE5EdFFDSZVatghtvhEcegaIiePBBKC/vzvufDWNeuJ/WzRORZhRQknZffeUerr39dti8GcaNc0HVL5pFWjdPRJJRQEnaWAvPPgvXXgvhsFui6De/gSOOyHRlIpILNElC0mL+fDjjDDjvPNh7b7dP0/PPK5xEpOMUUJJSn38Ol14KxcVuE8Hf/c6FVWlppisTkVyjLj5JiS1b4N574Y473JjTVVfBpEng8WS6MhHJVQoo2S3WwuzZbpxp2TK3RNHUqXD44ZmuTERynbr4ZJeFQnDaaTBqlNtuPRh0D98qnEQkFRRQ0mkrV8Ill0BJCXz0ETz0kBtnOvPMTFcmIvlEXXzSYZs3wz33wJ13ur2arr7ajTPtu2+mKxORfNSlAWWM8QBYayNd+bqye6yFWbNg/Hioq4NzznHjTMOGZboyEclnKQ8oY0w5EAY81trKFpf9wFjj9ukuAi6z1oZSXYOkRm1dAzNe/pI5jx7A+zU9GD4cHn/cPd8kIpJuKQ0oY8x4IGitDRljpgMtAypkrS2N3utXOGWv/30vwpjLNrJ+wSF03/srbpj8Fbdc25vu3TNdmYgUilRPkhgBRGIHxhhf4kVrbTh6vsxaG0zxa0sKbN7s1sw7+7S+rF94AH2/sZRDyl/ngBNWKpxEpEulewwq0sr5Eezcuop1D5YDHHrooemrSnZiLcyY4caZli+HM77byDLvu5i+X2obDBHJiFQHVDXgiR3EWkyJjDH+1r7YWhsAAgAlJSU2xbVJK957z60w/u67cPzx8Pvfw+mn96K27uvMC6/VNhgikhGpDqgAMDo6CaIqdtIYUx4NH3ABtjTFryu74LPPYOJEeOop2G8/t0/TRRcR78rTNhgikkkpDajo9PFYEIUSzgcS/rxT1550rU2b3LYXFRXQ2AjXXeeCqm/fTFcmIrKDHtQtINbCn/4EEybAp59CWRlMmQKHHZbpykREdqaljgrEvHlw0knw4x/DwIHwxhvu4VuFk4hkKwVUnlu+HH7yEzjxRLfa+GOPQXU1nHpqpisTEWmbuvjy1MaNbjmiKVOgqQmuv96NNe2zT6YrExHpGAVUnmlqgj/+0YXRZ5/B6NFuMsSQIZmuTESkc9TFl0fefdd15f3nf8L++8Nbb7mHbxVOIpKLFFB54JNP4Ec/cpMgli+HJ55wD99+85uZrkxEZNepiy+Hbdzouu+mTnXHkya5KeR9+mS2LhGRVFBA5aCmJnj6aTfOtGIFnH8+3HUXDB6c6cpERFJHXXw55p13YORIuPBCOOggePtt9/CtwklE8o0CKkfU1bmW0sknu9l5v/+9e/j25JMzXZmISHqoiy/Lffml676bNs0d33ST2xKjd+/M1iUikm4KqCxUW9fAO0vWsnb+AQTu7s3KlW6W3uTJoG2yRKRQKKCyTG1dA/9x08esmnMUWz/vzdeOb2T27B6ceGKmKxMR6VoKqCyybBmUX9yD5a+PpHufzQz8wXzKf7UPJ544LNOliYh0OQVUFtiwIWGcyfSh/6mL2adkKXvsbTlp2JBMlycikhEKqAxqaoInn3QLuX7+uVt1fPJkw6rtA5gXNtpqXUQKmgIqQ958E8aNg/nz3XNNzz0HJ5zgrh2MtloXEdFzUF0sHHY72Z52GqxZ41Yef+edHeEkIiKOAqqLrF/vliY6+mh4+WW49VZYtAguuACMyXR1IiLZR118abZ9u1td/IYbYNUqt0TRnXe6ZYpERKR1Cqg0ev11uPJK+Pvf3VYYL7wAI0ZkuioRkdygLr40WLoUzjsPzjgD6uvhmWfcoq4KJxGRjlNApdD69W4/pmOOgVdegdtvd+NMY8ZonElEpLPUxZcC27fDY4+5DQO/+AIuugjuuAMOPDDTlYmI5C4F1G569VU3zrRggdti/cUXoaQk01WJiOQ+dfHtosWL4Zxz4MwzYd06mDnTPXyrcBIRSQ0FVCetWwfXXgvHHgvBoJsyvmgRjBqlcSYRkVRSF18HNTbCo4/CjTe6FSAuvthNgjjggExXJiKSn9SC6oC5c8Hng5//HI46CmpqXFgpnERE0kcB1YbFi+Hss8Hvd1tiVFbCG2+4sBIRkfRSQCURicDVV7txpldfdXs1ffSRe/hW40wiIl1DY1AJGhvh4YfdOFN9PfzsZ3DbbbD//pmuTESk8KgFFTVnDhx/PFx+OXztaxAKubBSOImIZEbBB9THH8P3vw/f+Q5s2gSzZ8Nrr7mwEhGRzEl5QBljyo0xfmNMWSvXy6LXx6f6tTujocGtAPG1r7kHbCsq3DjTuedqnElEJBukNKCioVNjrQ0CpUmu+4Gi6PXKVL52RzU2woMPwrBhcN99cMklbrbe+PGwxx6ZqEhERJJJdQtqBBCJHRhjWk7ILo2e9wP+FL92u155BYYPh1/8wv0+fz5Mnw777dfVlYiISHvSPQYVaXHsAcKxFpYxxpN4Mdo9WGOMqVm9enXKili0CM46C777XfjqK3j2Wffw7fDhKXsJERFJsVQHVDUuhACw1oZbXK9t64uttQFrbYm1tmTgwIG7XUx9PfzqV26c6e23YepUWLjQLfKqcSYRkeyW6oAKACXRrr2q2EljTDm4AAJ80S6+KmttJMWvH3fz1I0cMmQ7DzxgufRSN850zTUaZxIRyRUpfVA3GjiB6GEo4Xwg4c9TUvmaydTWNfDQqytoKtqPQ85fxGUTj2XQoH7pflkREUmhvFxJYl54LXsPX8aeX19G927uuHiwAkpEJJfk5YO6I7392aNnN3p0g549ujHS2z/TJYmISCflZQuqeHA/nr50JPPCaxnp7a/Wk4hIDsrLgAIXUgomEZHclZddfCIikvsUUCIikpUUUCIikpUUUCIikpUUUCIikpUUUCIikpWMtTbTNSRljFkN1GW6jhQbAKzJdBFdQO8zv+h95pdse5+DrbVJVwfP2oDKR8aYGmttSabrSDe9z/yi95lfcul9qotPRESykgJKRESykgKqawXavyUv6H3mF73P/JIz71NjUCIikpXUghIRkaykgJK0MsZ4E3+X3KbPM79k++epgEoTY4zfGFPRxvXy6D1lXVlXqrX1Po0xHmC6MWZ611aVWsYYjzHGZ4wpM8aMb+WenP8823uf+fJ5Qvz/27LWPq98+Dyh7feZC5+nAipNrLVBIOm/SqJ/+Wui95R2aWEp1tb7jJpgrR1rrQ13VU1pMBqIWGsrgTHRv9hxefR5tvk+o3L+8zTG+ABP9H1OTHI9Lz7P9t5nVFZ/ngqozBgBRGIH0f+R8lVJ9F9x5ZkuZFdZawOJf4GttZEWt+TF59mB9wn58XmGgGD0PUxOcku+fJ7tvU/I8s9TAZUdIpkuIB2stZHoD70gMCrT9eyu6L+sO/I+ImkuJa1ae5/59HlGwzcIjOnA7ZG0FpNGbb3PXPg8FVCZUQ14YgfZ2rzeXdF+fE+m60gFY4wfqGzlct58nm29z3z5PI0x440x3ujn5E3ynvLi82zvfebC56mASpPoX3RvYvdAQjM6gGta+4CqTNSXKu28z5nRa35gVibqS4Vo/RXAdBLeR759nh14n3nxeeIC2BOdODAj1pWZb58n7b/PrP889aCuiIhkJbWgREQkKymgREQkKymgREQkKymgREQkKymgRFIo+tBjp5eOSVyKpqPL60SXsPFm6zpqIrtLASWSQtGHHos68zXRab6hhFNJv94YUxG9N35f9BkXf7L7RXKdAkok80rbexg0oZWUrLVU0yK4RPJCj0wXIJKvok/pjwbCgNdaG4gGTWKY1JCwakEbvLiHRndaF85aG4quKB/c3ZpFsolaUCLpUwHMjHb7DY2uTBBrAdXjgitMO2u9JYxJeYGhrdzm2d1iRbKNWlAi6ZNsLCkWTPUJS894WvsG0Wsha204+ufWFvWM7EadIllJLSiRFIq1kqJhMgEYHR0fWhrd/iCCa1lNTGgZRdr4Xg8njE95o9/b2+I+L26BU5G8ohaUSApFQ6g4ehjBLTyaqAy4zFobia4m7QWWtvG9RrU4TtbF57fWtnwdkZynFpRI1wqzY6VscF19gV3dWjzaUsvJ7SBE2qPVzEVEJCupBSUiIllJASUiIllJASUiIllJASUiIllJASUiIllJASUiIlnp/wFHxSUg+6wJDAAAAABJRU5ErkJggg==\n",
      "text/plain": "<Figure size 489.6x288 with 1 Axes>"
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig,ax=plt.subplots(figsize=(6.8,4))\n",
    "ax.plot(np.log(subregion_max_list),(von_Neumann_entropy_list[2]),'.')\n",
    "ax.set_xlabel(r'$\\log(|A|)$')\n",
    "ax.set_ylabel(r'$S_A$')\n",
    "lr=scipy.stats.linregress(np.log(subregion_max_list)[:10],(von_Neumann_entropy_list[2])[:10])\n",
    "ax.text(0.1,0.9,r'Fitted: $y={:.3f}~x+ {:.3f}$'.format(lr.slope,lr.intercept),transform=ax.transAxes)\n",
    "ax.text(0.15,0.8,r' $R^2={:f}$'.format(lr.rvalue),transform=ax.transAxes)\n",
    "ax.plot(np.log(subregion_max_list),lr.slope*np.log(subregion_max_list)+lr.intercept,'b')\n",
    "# fig.savefig('/mnt/d/kitp/Rp_SPT/2/critical_exponent.pdf',bbox_inches='tight')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/home/jake/anaconda3/lib/python3.8/site-packages/scipy/sparse/_index.py:82: SparseEfficiencyWarning: Changing the sparsity structure of a csr_matrix is expensive. lil_matrix is more efficient.\n",
      "  self._set_intXint(row, col, x.flat[0])\n"
     ]
    }
   ],
   "source": [
    "subregion_max_list=np.arange(2,398)\n",
    "entropy_all=[]\n",
    "mu=2\n",
    "von_Neumann_entropy_list[mu]=[]\n",
    "params=Params(mu=mu,Delta=1,L=400)\n",
    "for subregion_max in subregion_max_list:\n",
    "    entropy_all.append(params.von_Neumann_entropy(np.arange(subregion_max)))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": "[<matplotlib.lines.Line2D at 0x7f23cef62640>]"
     },
     "execution_count": 27,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": "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\n",
      "text/plain": "<Figure size 489.6x288 with 1 Axes>"
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "\n",
    "plt.plot(subregion_max_list,entropy_all,'.')\n",
    "# plt.xlim([0,40])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Mutual information"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 28,
   "metadata": {},
   "outputs": [],
   "source": [
    "MI_list={}"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 29,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/home/jake/anaconda3/lib/python3.8/site-packages/scipy/sparse/_index.py:82: SparseEfficiencyWarning: Changing the sparsity structure of a csr_matrix is expensive. lil_matrix is more efficient.\n",
      "  self._set_intXint(row, col, x.flat[0])\n"
     ]
    }
   ],
   "source": [
    "dist_list=np.arange(10,50)\n",
    "mu=0\n",
    "MI_list[mu]=[]\n",
    "params=Params(mu=mu,Delta=0.05,L=400)\n",
    "for dist in dist_list:\n",
    "    MI_list[mu].append(params.mutual_information(np.arange(10),np.arange(dist,dist+10)))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 33,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": "<Figure size 489.6x288 with 2 Axes>"
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig,ax1=plt.subplots(figsize=(6.8,4))\n",
    "\n",
    "color = 'tab:red'\n",
    "ax1.set_xlabel('distance between A and B')\n",
    "ax1.set_ylabel(r'mutual information $I(A;B)$', color=color)\n",
    "ax1.plot(dist_list,MI_list[mu],'.', color=color)\n",
    "ax1.tick_params(axis='y', labelcolor=color)\n",
    "ax1.set_ylim([-0.01,1.4])\n",
    "ax2 = ax1.twinx()  \n",
    "\n",
    "color = 'tab:blue'\n",
    "ax2.set_ylabel(r'$\\log(I(A;B))$', color=color)  \n",
    "ax2.plot(dist_list,np.log(MI_list[mu]), '.',color=color)\n",
    "ax2.tick_params(axis='y', labelcolor=color)\n",
    "mask=(dist_list>20)*(dist_list<50)\n",
    "lr=scipy.stats.linregress(dist_list[mask],np.log(MI_list[mu])[mask])\n",
    "\n",
    "ax2.text(.6,.8,r'Fitted: $y={:.4f}~x+{:.4f}$'.format(lr.slope,lr.intercept),transform=ax2.transAxes)\n",
    "ax2.text(.68,.7,r'$R^2={:f}$'.format(lr.rvalue),transform=ax2.transAxes)\n",
    "ax2.plot(dist_list,lr.slope*dist_list+lr.intercept,color=color)\n",
    "fig.tight_layout()\n",
    "\n",
    "fig.savefig('/mnt/d/kitp/Rp_SPT/2/MI_mu0.pdf',bbox_inches='tight')\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 34,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/home/jake/anaconda3/lib/python3.8/site-packages/scipy/sparse/_index.py:82: SparseEfficiencyWarning: Changing the sparsity structure of a csr_matrix is expensive. lil_matrix is more efficient.\n",
      "  self._set_intXint(row, col, x.flat[0])\n"
     ]
    }
   ],
   "source": [
    "dist_list=np.arange(10,50)\n",
    "mu=1\n",
    "MI_list[mu]=[]\n",
    "params=Params(mu=mu,Delta=0.05,L=400)\n",
    "for dist in dist_list:\n",
    "    MI_list[mu].append(params.mutual_information(np.arange(10),np.arange(dist,dist+10)))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 37,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": "<Figure size 489.6x288 with 2 Axes>"
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig,ax1=plt.subplots(figsize=(6.8,4))\n",
    "\n",
    "color = 'tab:red'\n",
    "ax1.set_xlabel('distance between A and B')\n",
    "ax1.set_ylabel(r'mutual information $I(A;B)$', color=color)\n",
    "ax1.plot(dist_list,MI_list[mu],'.', color=color)\n",
    "ax1.tick_params(axis='y', labelcolor=color)\n",
    "ax1.set_ylim([-0.01,1.4])\n",
    "\n",
    "ax2 = ax1.twinx()  \n",
    "\n",
    "color = 'tab:blue'\n",
    "ax2.set_ylabel(r'$\\log(I(A;B))$', color=color)  \n",
    "ax2.plot(dist_list,np.log(MI_list[mu]),'.',color=color)\n",
    "ax2.tick_params(axis='y', labelcolor=color)\n",
    "mask=(dist_list>20)*(dist_list<50)\n",
    "lr=scipy.stats.linregress(dist_list[mask],np.log(MI_list[mu])[mask])\n",
    "\n",
    "ax2.text(.6,.8,r'Fitted: $y={:.4f}~x+{:.4f}$'.format(lr.slope,lr.intercept),transform=ax2.transAxes)\n",
    "ax2.text(.68,.7,r'$R^2={:f}$'.format(lr.rvalue),transform=ax2.transAxes)\n",
    "ax2.plot(dist_list,lr.slope*dist_list+lr.intercept,color=color)\n",
    "\n",
    "fig.tight_layout()\n",
    "\n",
    "\n",
    "fig.savefig('/mnt/d/kitp/Rp_SPT/2/MI_mu1.pdf',bbox_inches='tight')\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 47,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/home/jake/anaconda3/lib/python3.8/site-packages/scipy/sparse/_index.py:82: SparseEfficiencyWarning: Changing the sparsity structure of a csr_matrix is expensive. lil_matrix is more efficient.\n",
      "  self._set_intXint(row, col, x.flat[0])\n"
     ]
    }
   ],
   "source": [
    "dist_list=np.arange(10,20)\n",
    "mu=3\n",
    "MI_list[mu]=[]\n",
    "params=Params(mu=mu,Delta=0.05,L=400)\n",
    "for dist in dist_list:\n",
    "    MI_list[mu].append(params.mutual_information(np.arange(10),np.arange(dist,dist+10)))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 52,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": "<Figure size 489.6x288 with 2 Axes>"
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig,ax1=plt.subplots(figsize=(6.8,4))\n",
    "\n",
    "color = 'tab:red'\n",
    "ax1.set_xlabel('distance between A and B')\n",
    "ax1.set_ylabel(r'mutual information $I(A;B)$', color=color)\n",
    "ax1.plot(dist_list,MI_list[mu],'.', color=color)\n",
    "ax1.tick_params(axis='y', labelcolor=color)\n",
    "ax1.set_ylim([-1e-4,0.003])\n",
    "\n",
    "ax2 = ax1.twinx()  \n",
    "\n",
    "color = 'tab:blue'\n",
    "ax2.set_ylabel(r'$\\log(I(A;B))$', color=color)  \n",
    "ax2.plot(dist_list,np.log(MI_list[mu]),'.', color=color)\n",
    "ax2.tick_params(axis='y', labelcolor=color)\n",
    "\n",
    "lr=scipy.stats.linregress(dist_list,np.log(MI_list[mu]))\n",
    "\n",
    "ax2.text(.6,.8,r'Fitted: $y={:.4f}~x+{:.4f}$'.format(lr.slope,lr.intercept),transform=ax2.transAxes)\n",
    "ax2.text(.68,.7,r'$R^2={:f}$'.format(lr.rvalue),transform=ax2.transAxes)\n",
    "ax2.plot(dist_list,lr.slope*dist_list+lr.intercept,color=color)\n",
    "\n",
    "fig.tight_layout()\n",
    "\n",
    "\n",
    "fig.savefig('/mnt/d/kitp/Rp_SPT/2/MI_mu3.pdf',bbox_inches='tight')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 53,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/home/jake/anaconda3/lib/python3.8/site-packages/scipy/sparse/_index.py:82: SparseEfficiencyWarning: Changing the sparsity structure of a csr_matrix is expensive. lil_matrix is more efficient.\n",
      "  self._set_intXint(row, col, x.flat[0])\n"
     ]
    }
   ],
   "source": [
    "dist_list=np.arange(10,50)\n",
    "mu=2\n",
    "MI_list[mu]=[]\n",
    "params=Params(mu=mu,Delta=0.05,L=400)\n",
    "for dist in dist_list:\n",
    "    MI_list[mu].append(params.mutual_information(np.arange(10),np.arange(dist,dist+10)))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 63,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": "<Figure size 489.6x288 with 2 Axes>"
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig=plt.figure()\n",
    "ax1=fig.add_subplot(111, label=\"1\")\n",
    "ax2=fig.add_subplot(111, label=\"2\",frame_on=False)\n",
    "\n",
    "\n",
    "color = 'tab:red'\n",
    "ax1.set_xlabel('distance between A and B',color=color)\n",
    "ax1.set_ylabel(r'mutual information $I(A;B)$', color=color)\n",
    "ax1.plot(dist_list,MI_list[mu],'.', color=color)\n",
    "ax1.tick_params(axis='x', labelcolor=color)\n",
    "ax1.tick_params(axis='y', labelcolor=color)\n",
    "\n",
    "\n",
    "color = 'tab:blue'\n",
    "\n",
    "ax2.plot(np.log(dist_list),np.log(MI_list[mu]),'.', color=color)\n",
    "ax2.xaxis.tick_top()\n",
    "ax2.yaxis.tick_right()\n",
    "ax2.xaxis.set_label_position('top') \n",
    "ax2.yaxis.set_label_position('right') \n",
    "ax2.set_xlabel(r'log distance', color=color) \n",
    "ax2.set_ylabel(r'$\\log(I(A;B))$', color=color)  \n",
    "ax2.tick_params(axis='x', labelcolor=color)\n",
    "ax2.tick_params(axis='y', labelcolor=color)\n",
    "mask=(dist_list>5)&(dist_list<30)\n",
    "lr=scipy.stats.linregress(np.log(dist_list)[mask],np.log(MI_list[mu])[mask])\n",
    "\n",
    "ax2.text(.6,.8,r'Fitted: $y={:.4f}~x+{:.4f}$'.format(lr.slope,lr.intercept),transform=ax2.transAxes)\n",
    "ax2.text(.68,.7,r'$R^2={:f}$'.format(lr.rvalue),transform=ax2.transAxes)\n",
    "ax2.plot(np.log(dist_list),lr.slope*np.log(dist_list)+lr.intercept,color=color)\n",
    "\n",
    "ax2.axvline(x=np.log(dist_list)[mask][0],lw=1,ls='--')\n",
    "ax2.axvline(x=np.log(dist_list)[mask][-1],lw=1,ls='--')\n",
    "\n",
    "fig.tight_layout()\n",
    "\n",
    "\n",
    "fig.savefig('/mnt/d/kitp/Rp_SPT/2/MI_mu2.pdf',bbox_inches='tight')\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 65,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": "array([2.30258509, 3.40119738])"
     },
     "execution_count": 65,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.log([10,30])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Class"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 71,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": "0.0"
     },
     "execution_count": 71,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "2*np.heaviside(0,1/2)-1"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 72,
   "metadata": {},
   "outputs": [],
   "source": [
    "class Params:\n",
    "    '''\n",
    "    example: params=Params(mu=2)\n",
    "    '''\n",
    "    def __init__(self,\n",
    "    mu=1,\n",
    "    t=1,\n",
    "    Delta=1,\n",
    "    L=100,\n",
    "    T=0,\n",
    "    bc=1    # 0: open boundary condition; >0: PBC; <0: APBC\n",
    "    ):\n",
    "        self.mu=mu\n",
    "        self.t=t\n",
    "        self.Delta=Delta\n",
    "        self.L=L\n",
    "        self.tau_z=sp.dia_matrix(np.diag([1,-1]))\n",
    "        self.tau_y=sp.dia_matrix(np.array([[0,-1j],[1j,0]]))\n",
    "        self.pbc=pbc\n",
    "        self.T=T\n",
    "        self.band1sm=sp.diags([1],[1],(L,L)).tocsr()\n",
    "        self.bandm1sm=sp.diags([1],[-1],(L,L)).tocsr()\n",
    "        self.band1sm[-1,0]=1*(2*np.heaviside(bc,1/2)-1)\n",
    "        self.bandm1sm[0,-1]=1*(2*np.heaviside(bc,1/2)-1)\n",
    "        self.Hamiltonian=-self.mu*sp.kron(self.tau_z,sp.identity(self.L))-sp.kron(self.t*self.tau_z+1j*self.Delta*self.tau_y,self.band1sm)-sp.kron(self.t*self.tau_z-1j*self.Delta*self.tau_y,self.bandm1sm)\n",
    "    \n",
    "    def bandstructure(self):        \n",
    "        val,vec=la.eigh(self.Hamiltonian.toarray())\n",
    "        sortindex=np.argsort(val)\n",
    "        self.val=val[sortindex]\n",
    "        self.vec=vec[:,sortindex]\n",
    "\n",
    "    def fermi_dist(self,energy,E_F):      \n",
    "        if self.T==0:\n",
    "            return np.heaviside(E_F-energy,0)\n",
    "        else:\n",
    "            return 1/(1+np.exp((energy-E_F)/self.T)) \n",
    "\n",
    "\n",
    "    def covariance_matrix(self,E_F=0):\n",
    "        if not (hasattr(self,'val') and hasattr(self,'vec')):\n",
    "            self.bandstructure()\n",
    "        occupancy=self.fermi_dist(self.val,E_F)\n",
    "        occupancy_mat=np.matlib.repmat(self.fermi_dist(self.val,E_F),self.vec.shape[0],1)\n",
    "        self.C=np.real((occupancy_mat*self.vec)@self.vec.T.conj())\n",
    "\n",
    "    def c_subregion(self,subregion):\n",
    "        if not hasattr(self,'C'):\n",
    "            self.covariance_matrix()\n",
    "        XX,YY=np.meshgrid(np.arange(2*self.L),np.arange(2*self.L))\n",
    "        mask_hh=np.isin(XX,subregion)*np.isin(YY,subregion)\n",
    "        mask_hp=np.isin(XX,subregion)*np.isin(YY,subregion+self.L)\n",
    "        mask_ph=np.isin(XX,subregion+self.L)*np.isin(YY,subregion)\n",
    "        mask_pp=np.isin(XX,subregion+self.L)*np.isin(YY,subregion+self.L)\n",
    "        mask=mask_hh+mask_hp+mask_ph+mask_pp\n",
    "        return self.C[mask].reshape((2*subregion.shape[0],2*subregion.shape[0]))\n",
    "\n",
    "    def von_Neumann_entropy(self,subregion):\n",
    "        c_A=self.c_subregion(subregion)\n",
    "        val,vec=la.eigh(c_A)\n",
    "        self.val_sh=val\n",
    "        val=np.sort(val)[:subregion.shape[0]]\n",
    "        return np.real(-np.sum(val*np.log(val+1e-18j))-np.sum((1-val)*np.log(1-val+1e-18j)))\n",
    "\n",
    "    def mutual_information(self,subregion_A,subregion_B):\n",
    "        s_A=self.von_Neumann_entropy(subregion_A)\n",
    "        s_B=self.von_Neumann_entropy(subregion_B)\n",
    "        subregion_AB=np.hstack([subregion_A,subregion_B])\n",
    "        s_AB=self.von_Neumann_entropy(subregion_AB)\n",
    "        return s_A+s_B-s_AB\n",
    "    "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Test"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 40,
   "metadata": {},
   "outputs": [],
   "source": [
    "params=Params(mu=0,L=200,Delta=0.1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 41,
   "metadata": {},
   "outputs": [],
   "source": [
    "params.covariance_matrix(0)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 42,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "1.2367968869128296"
      ]
     },
     "execution_count": 42,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "params.von_Neumann_entropy(np.arange(50))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([0.01298925, 0.05531669, 0.94468331, 0.98701075])"
      ]
     },
     "execution_count": 10,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "params.val_sh"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 116,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "4.7860059782522946e-05"
      ]
     },
     "execution_count": 116,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "params.mutual_information(np.arange(2),np.arange(2)+10)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 117,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "7.179432937043373e-09"
      ]
     },
     "execution_count": 117,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "params.mutual_information(np.arange(2),np.arange(2)+20)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 120,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "1.2989609388114332e-14"
      ]
     },
     "execution_count": 120,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "params.mutual_information(np.arange(2),np.arange(2)+50)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([-4.33055857, -2.83777501,  2.83777501,  4.33055857])"
      ]
     },
     "execution_count": 11,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.log(params.val_sh/(1-params.val_sh))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 89,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.998320705473697"
      ]
     },
     "execution_count": 89,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "params.val_sh[0]+params.val_sh[-1]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 90,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.9816792945263035"
      ]
     },
     "execution_count": 90,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "params.val_sh[1]+params.val_sh[-2]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 92,
   "metadata": {},
   "outputs": [],
   "source": [
    "z=params.c_subregion(np.arange(2))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 93,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[ 8.13283706e-01,  1.11129481e-01,  6.20482392e-17,\n",
       "         2.12154225e-01],\n",
       "       [ 1.11129481e-01,  8.13283706e-01, -2.12154225e-01,\n",
       "        -1.36907625e-16],\n",
       "       [ 6.20482392e-17, -2.12154225e-01,  1.76716294e-01,\n",
       "        -1.01129481e-01],\n",
       "       [ 2.12154225e-01, -1.36907625e-16, -1.01129481e-01,\n",
       "         1.76716294e-01]])"
      ]
     },
     "execution_count": 93,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "z"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 52,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[ 0.5 , -0.25],\n",
       "       [-0.25,  0.5 ]])"
      ]
     },
     "execution_count": 52,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "z[2:2+2,2:2+2]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 56,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[ 0.00000000e+00,  2.50000000e-01],\n",
       "       [-2.50000000e-01, -1.91753388e-17]])"
      ]
     },
     "execution_count": 56,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "z[:2,2:2+2]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 57,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[ 0.00000000e+00, -2.50000000e-01],\n",
       "       [ 2.50000000e-01, -1.91753388e-17]])"
      ]
     },
     "execution_count": 57,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "z[2:2+2,:2]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 46,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[0.5 , 0.25],\n",
       "       [0.25, 0.5 ]])"
      ]
     },
     "execution_count": 46,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "params.C[:2,:2]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 50,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[ 0.5 , -0.25],\n",
       "       [-0.25,  0.5 ]])"
      ]
     },
     "execution_count": 50,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "params.C[params.L:params.L+2,params.L:params.L+2]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 53,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[ 0.00000000e+00,  2.50000000e-01],\n",
       "       [-2.50000000e-01, -1.91753388e-17]])"
      ]
     },
     "execution_count": 53,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "params.C[:2,params.L:params.L+2]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 54,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[ 0.00000000e+00, -2.50000000e-01],\n",
       "       [ 2.50000000e-01, -1.91753388e-17]])"
      ]
     },
     "execution_count": 54,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "params.C[params.L:params.L+2,:2]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 33,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(80.0, 120.0, 80.0, 120.0)"
      ]
     },
     "execution_count": 33,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
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      "text/plain": "<Figure size 432x288 with 1 Axes>"
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     "metadata": {
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   ],
   "source": [
    "plt.imshow(params.C)\n",
    "plt.axis([80,120,80,120])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/home/jake/anaconda3/lib/python3.8/site-packages/scipy/sparse/_index.py:82: SparseEfficiencyWarning: Changing the sparsity structure of a csr_matrix is expensive. lil_matrix is more efficient.\n",
      "  self._set_intXint(row, col, x.flat[0])\n"
     ]
    }
   ],
   "source": [
    "mulist=np.linspace(0,4,50)\n",
    "eigvallist=[]\n",
    "for mu in mulist:\n",
    "    params=Params(mu=mu,n=100)\n",
    "    params.bandstructure()\n",
    "    eigvallist.append(params.val)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/home/jake/anaconda3/lib/python3.8/site-packages/scipy/sparse/_index.py:82: SparseEfficiencyWarning: Changing the sparsity structure of a csr_matrix is expensive. lil_matrix is more efficient.\n",
      "  self._set_intXint(row, col, x.flat[0])\n"
     ]
    }
   ],
   "source": [
    "mulist=np.linspace(0,4,50)\n",
    "eigvallist2=[]\n",
    "for mu in mulist:\n",
    "    params=Params(mu=mu,n=100,pbc=False)\n",
    "    params.bandstructure()\n",
    "    eigvallist2.append(params.val)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
    {
     "data": {
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      "text/plain": "<Figure size 432x288 with 1 Axes>"
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig,ax=plt.subplots()\n",
    "for index in range(eigvallist[0].shape[0]):\n",
    "    ax.plot(mulist,np.array(eigvallist)[:,index],'k')\n",
    "    ax.set_ylim([-2,2])\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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      "text/plain": "<Figure size 432x288 with 1 Axes>"
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig,ax=plt.subplots()\n",
    "for index in range(eigvallist2[0].shape[0]):\n",
    "    ax.plot(mulist,np.array(eigvallist2)[:,index],'k')\n",
    "    ax.set_ylim([-2,2])\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# $1+\\delta$, $1-\\delta$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 28,
   "metadata": {},
   "outputs": [],
   "source": [
    "def wrapper(delta,**kwargs):\n",
    "    mu=2*(1-delta)\n",
    "    t=-(1+delta)\n",
    "    Delta=-(1+delta)\n",
    "    return Params(**kwargs,mu=mu,t=t,Delta=Delta)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "{'L': 16}\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/home/jake/anaconda3/lib/python3.8/site-packages/scipy/sparse/_index.py:82: SparseEfficiencyWarning: Changing the sparsity structure of a csr_matrix is expensive. lil_matrix is more efficient.\n",
      "  self._set_intXint(row, col, x.flat[0])\n"
     ]
    }
   ],
   "source": [
    "params=wrapper(0-0.1,L=16)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [],
   "source": [
    "params.bandstructure()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## open bc"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 37,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/home/jake/anaconda3/lib/python3.8/site-packages/scipy/sparse/_index.py:82: SparseEfficiencyWarning: Changing the sparsity structure of a csr_matrix is expensive. lil_matrix is more efficient.\n",
      "  self._set_intXint(row, col, x.flat[0])\n"
     ]
    },
    {
     "data": {
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\n",
      "text/plain": "<Figure size 489.6x288 with 1 Axes>"
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "val_list=np.linspace(-1,1,100)\n",
    "eigvallist2=[]\n",
    "for val in val_list:\n",
    "    params=wrapper(val,L=16,bc=0)\n",
    "    params.bandstructure()\n",
    "    eigvallist2.append(params.val)\n",
    "\n",
    "    \n",
    "fig,ax=plt.subplots()\n",
    "for index in range(eigvallist2[0].shape[0]):\n",
    "    ax.plot(val_list,np.array(eigvallist2)[:,index],'k')\n",
    "    # ax.set_ylim([-2,2])\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## periodic bc"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 35,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/home/jake/anaconda3/lib/python3.8/site-packages/scipy/sparse/_index.py:82: SparseEfficiencyWarning: Changing the sparsity structure of a csr_matrix is expensive. lil_matrix is more efficient.\n",
      "  self._set_intXint(row, col, x.flat[0])\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": "<Figure size 489.6x288 with 1 Axes>"
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "val_list=np.linspace(-1,1,100)\n",
    "eigvallist2=[]\n",
    "for val in val_list:\n",
    "    params=wrapper(val,L=16,bc=1)\n",
    "    params.bandstructure()\n",
    "    eigvallist2.append(params.val)\n",
    "\n",
    "    \n",
    "fig,ax=plt.subplots()\n",
    "for index in range(eigvallist2[0].shape[0]):\n",
    "    ax.plot(val_list,np.array(eigvallist2)[:,index],'k')\n",
    "    # ax.set_ylim([-2,2])\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## anti-periodic bc"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 36,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/home/jake/anaconda3/lib/python3.8/site-packages/scipy/sparse/_index.py:82: SparseEfficiencyWarning: Changing the sparsity structure of a csr_matrix is expensive. lil_matrix is more efficient.\n",
      "  self._set_intXint(row, col, x.flat[0])\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": "<Figure size 489.6x288 with 1 Axes>"
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "val_list=np.linspace(-1,1,100)\n",
    "eigvallist2=[]\n",
    "for val in val_list:\n",
    "    params=wrapper(val,L=16,bc=-1)\n",
    "    params.bandstructure()\n",
    "    eigvallist2.append(params.val)\n",
    "\n",
    "    \n",
    "fig,ax=plt.subplots()\n",
    "for index in range(eigvallist2[0].shape[0]):\n",
    "    ax.plot(val_list,np.array(eigvallist2)[:,index],'k')\n",
    "    # ax.set_ylim([-2,2])\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## test"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 49,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/home/jake/anaconda3/lib/python3.8/site-packages/scipy/sparse/_index.py:82: SparseEfficiencyWarning: Changing the sparsity structure of a csr_matrix is expensive. lil_matrix is more efficient.\n",
      "  self._set_intXint(row, col, x.flat[0])\n"
     ]
    }
   ],
   "source": [
    "params=wrapper(0-0.1,L=16,bc=-1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 50,
   "metadata": {},
   "outputs": [],
   "source": [
    "params.covariance_matrix()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 51,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": "<matplotlib.image.AxesImage at 0x7f86391cf550>"
     },
     "execution_count": 51,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": "<Figure size 489.6x288 with 1 Axes>"
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.imshow(params.C)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 52,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": "array([[ 8.99463417e-01, -4.45891018e-02,  1.68833179e-16,\n        -1.85983093e-01],\n       [-4.45891018e-02,  8.99463417e-01,  1.85983093e-01,\n        -4.74886076e-16],\n       [ 1.68833179e-16,  1.85983093e-01,  1.00536583e-01,\n         4.45891018e-02],\n       [-1.85983093e-01, -4.74886076e-16,  4.45891018e-02,\n         1.00536583e-01]])"
     },
     "execution_count": 52,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "params.c_subregion(np.array([4,5]))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 83,
   "metadata": {},
   "outputs": [],
   "source": [
    "def projection(s,i,j):\n",
    "    '''\n",
    "    s= 0,1 occupancy number\n",
    "    i,j: adjacent pair of Majorana\n",
    "    flow is from alpha_{i,j} to gamma_{i,j}\n",
    "\n",
    "    return: the basis are ordered as gamma_i,gamma_j,alpha_j,alpha_i\n",
    "    '''\n",
    "    assert (s==0 or s==1),\"s={} is either 0 or 1\".format(s)\n",
    "    blkmat=(np.array([[0,-(-1)**s],[(-1)**s,0]]))\n",
    "    return sp.bmat([[blkmat,None],[None,blkmat.T]])\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 84,
   "metadata": {},
   "outputs": [],
   "source": [
    "z=projection(1,0,0)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 85,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": "<4x4 sparse matrix of type '<class 'numpy.int64'>'\n\twith 4 stored elements in COOrdinate format>"
     },
     "execution_count": 85,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "z"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 86,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": "array([[ 0,  1,  0,  0],\n       [-1,  0,  0,  0],\n       [ 0,  0,  0, -1],\n       [ 0,  0,  1,  0]])"
     },
     "execution_count": 86,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "z.toarray()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 87,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": "array([[ 0, -1,  0,  0],\n       [ 1,  0,  0,  0],\n       [ 0,  0,  0,  1],\n       [ 0,  0, -1,  0]])"
     },
     "execution_count": 87,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "projection(0,0,0).toarray()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 89,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": "<4x4 sparse matrix of type '<class 'numpy.int64'>'\n\twith 4 stored elements in COOrdinate format>"
     },
     "execution_count": 89,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "projection(1,0,0)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3.8.5 64-bit ('base': conda)",
   "name": "python385jvsc74a57bd06aee4f39eba147985a2c1cbf1db4ebecc02362fa8877deaa860706b7b1b97f3d"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.8.5"
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 "nbformat": 4,
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}