14_FasedeZak-SSH.ipynb

{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Populating the interactive namespace from numpy and matplotlib\n"
     ]
    }
   ],
   "source": [
    "%pylab inline"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "mpl.rcParams.update({'font.size': 18, 'text.usetex': True})\n",
    "mpl.rcParams.update({'axes.linewidth':1.5})\n",
    "mpl.rcParams.update({'axes.labelsize':'large'})\n",
    "mpl.rcParams.update({'xtick.major.size':6})\n",
    "mpl.rcParams.update({'xtick.minor.size':4})\n",
    "mpl.rcParams.update({'ytick.major.size':6})\n",
    "mpl.rcParams.update({'ytick.minor.size':4})\n",
    "mpl.rcParams.update({'xtick.major.width':1.5})\n",
    "mpl.rcParams.update({'xtick.minor.width':1.0})\n",
    "mpl.rcParams.update({'ytick.major.width':1.5})\n",
    "mpl.rcParams.update({'ytick.minor.width':1.0})\n",
    "mpl.rcParams.update({'legend.frameon':False,'legend.framealpha':0.0})\n",
    "# mpl.rcParams.update({'axes.grid':True})"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Modelo SSH\n",
    "\n",
    "\\begin{eqnarray}\n",
    "H(k) = \\left[\n",
    "\\begin{array}{cc}\n",
    "0& v+we^{-ik}\\\\\n",
    "v+we^{ik}&0\n",
    "\\end{array}\n",
    "\\right]\n",
    "\\end{eqnarray}"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [],
   "source": [
    "def HamSSH(k,v=0.5,w=1.0):\n",
    "    H = np.array([[0,v+w*exp(-1J*k)],\n",
    "                  [v+w*exp(1J*k),0]])\n",
    "    return H"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Estructura de Bandas"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 60,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 288x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "v = 1.0; w = 0.5\n",
    "kpath = linspace(-pi,pi,1000)\n",
    "E = []\n",
    "for k in kpath:\n",
    "    H     = HamSSH(k,v,w)\n",
    "    Ek,vk = eigh(H)\n",
    "    E.append(Ek)\n",
    "E = array(E)\n",
    "\n",
    "fig,ax = plt.subplots(ncols=1,nrows=1,figsize=(4,4))\n",
    "ax.plot(kpath,E.T[0],c='b',lw=4)\n",
    "ax.plot(kpath,E.T[1],c='b',lw=4)\n",
    "ax.set_xlabel(r'$k$');\n",
    "ax.set_ylabel(r'$E$');\n",
    "ax.set_xticks([-pi,0,pi]);\n",
    "ax.set_xticklabels([r'$-\\pi$',r'$0$',r'$\\pi$']);\n",
    "ax.set_yticks([-2,0,2]);\n",
    "fig.tight_layout()\n",
    "fig.savefig(\"Bandas1.png\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 61,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 288x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "v = 1.0; w = 1.0\n",
    "kpath = linspace(-pi,pi,1000)\n",
    "E = []\n",
    "for k in kpath:\n",
    "    H     = HamSSH(k,v,w)\n",
    "    Ek,vk = eigh(H)\n",
    "    E.append(Ek)\n",
    "E = array(E)\n",
    "\n",
    "fig,ax = plt.subplots(ncols=1,nrows=1,figsize=(4,4))\n",
    "ax.plot(kpath,E.T[0],c='b',lw=4)\n",
    "ax.plot(kpath,E.T[1],c='b',lw=4)\n",
    "ax.set_xlabel(r'$k$');\n",
    "ax.set_ylabel(r'$E$');\n",
    "ax.set_xticks([-pi,0,pi]);\n",
    "ax.set_xticklabels([r'$-\\pi$',r'$0$',r'$\\pi$']);\n",
    "ax.set_yticks([-2,0,2]);\n",
    "fig.tight_layout()\n",
    "fig.savefig(\"Bandas2.png\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 62,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 288x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "v = 0.5; w = 1.0\n",
    "kpath = linspace(-pi,pi,1000)\n",
    "E = []\n",
    "for k in kpath:\n",
    "    H     = HamSSH(k,v,w)\n",
    "    Ek,vk = eigh(H)\n",
    "    E.append(Ek)\n",
    "E = array(E)\n",
    "\n",
    "fig,ax = plt.subplots(ncols=1,nrows=1,figsize=(4,4))\n",
    "ax.plot(kpath,E.T[0],c='b',lw=4)\n",
    "ax.plot(kpath,E.T[1],c='b',lw=4)\n",
    "ax.set_xlabel(r'$k$');\n",
    "ax.set_ylabel(r'$E$');\n",
    "ax.set_xticks([-pi,0,pi]);\n",
    "ax.set_xticklabels([r'$-\\pi$',r'$0$',r'$\\pi$']);\n",
    "ax.set_yticks([-2,0,2]);\n",
    "fig.tight_layout()\n",
    "fig.savefig(\"Bandas3.png\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [],
   "source": [
    "def GetPhase(v,w):\n",
    "    kpath = linspace(-pi,pi,1000)\n",
    "\n",
    "    Ek,vk = eigh(HamSSH(kpath[0],v,w))\n",
    "    u0    = vk.T[Ek<0]\n",
    "    Ek,vk = eigh(HamSSH(kpath[1],v,w))\n",
    "    u1    = vk.T[Ek<0]\n",
    "    Prod  = np.vdot(u0,u1)\n",
    "\n",
    "    un1   = u1\n",
    "    for k in kpath[2:]:\n",
    "        H     = HamSSH(k,v,w)\n",
    "        Ek,vk = eigh(H)\n",
    "        un    = vk.T[Ek<0]\n",
    "        Prod *= np.vdot(un1,un)\n",
    "        # Update\n",
    "        un1   = un\n",
    "    ϕ = imag( log(Prod) )\n",
    "    \n",
    "    return ϕ"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [],
   "source": [
    "w = 1.0\n",
    "vpath = linspace(0,3.0,80)\n",
    "ϕv    = []\n",
    "for v in vpath:\n",
    "    ϕ = GetPhase(v,w)\n",
    "    ϕv.append( abs(ϕ) )\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 288x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig, axes = plt.subplots(ncols=1,nrows=1,figsize=(4.0,4.0))\n",
    "axes.scatter(vpath,ϕv,alpha=0.6,facecolors='none',edgecolors='b')\n",
    "axes.set_xlabel(r\"$v/w$\",size=24)\n",
    "axes.set_ylabel(r'$\\phi$',size=24)\n",
    "axes.set_yticks([0,pi])\n",
    "axes.plot([1,1],[-1,1.1*pi],'--',c='k')\n",
    "# axes.plot([-1,-1],[-1,1.1*pi],'--',c='k')\n",
    "axes.set_yticks([0,pi])\n",
    "axes.set_ylim(-0.2,pi+0.2)\n",
    "axes.set_yticklabels([r'$0$',r'$\\pi$'])\n",
    "fig.tight_layout()\n",
    "fig.savefig('zak.png')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
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   "language": "python",
   "name": "python3"
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   "hotkeys": {
    "equation": "Ctrl-E",
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  "toc": {
   "base_numbering": 1,
   "nav_menu": {},
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   "skip_h1_title": false,
   "title_cell": "Table of Contents",
   "title_sidebar": "Contents",
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   "toc_position": {},
   "toc_section_display": true,
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  },
  "varInspector": {
   "cols": {
    "lenName": 16,
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   "kernels_config": {
    "python": {
     "delete_cmd_postfix": "",
     "delete_cmd_prefix": "del ",
     "library": "var_list.py",
     "varRefreshCmd": "print(var_dic_list())"
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     "delete_cmd_postfix": ") ",
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