figures.ipynb

{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "import sys\n",
    "import os\n",
    "path_data = 'data/' \n",
    "path_figures = 'figures/'\n",
    "            \n",
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "import matplotlib.colors as colors\n",
    "import matplotlib.gridspec as gridspec\n",
    "from matplotlib import rc\n",
    "from matplotlib.ticker import FormatStrFormatter\n",
    "from matplotlib.collections import LineCollection\n",
    "from matplotlib.colors import ListedColormap, BoundaryNorm\n",
    "from mpl_toolkits.axes_grid1.inset_locator import inset_axes\n",
    "import matplotlib.ticker as ticker\n",
    "\n",
    "def Fibonacci(iterations):\n",
    "    \n",
    "    \"\"\"Return Fibonacci sequence number depending on the iterations\"\"\"\n",
    "    \n",
    "    Fn1 = 0\n",
    "    Fn = 1\n",
    "    for n in range(iterations):\n",
    "        Fn2 = Fn1\n",
    "        Fn1 = Fn\n",
    "        Fn = Fn1 + Fn2  \n",
    "        \n",
    "    return Fn1, Fn\n",
    "\n",
    "fs = 45\n",
    "plt.rc('xtick',labelsize=fs)\n",
    "plt.rc('ytick',labelsize=fs)\n",
    "plt.rc('text', usetex=True)\n",
    "plt.rc('font', family='serif')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# FIGURE 1 - SHORT RANGE KITAEV CHAIN"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "color_list = ['lightcoral','dodgerblue','seagreen']\n",
    "marker_list = ['^-.', 'X--', 'd:']\n",
    "\n",
    "##############################################\n",
    "fig = plt.figure(figsize=(18, 23))\n",
    "\n",
    "gs_plot = gridspec.GridSpec(7, 11, figure=fig)\n",
    "gs_plot.update(wspace=0.5)\n",
    "gs_plot.update(hspace=0.2)\n",
    "\n",
    "gs_plot2 = gridspec.GridSpec(7, 22, figure=fig)\n",
    "gs_plot2.update(wspace=0.2)\n",
    "gs_plot2.update(hspace=0.2)\n",
    "\n",
    "#############################################\n",
    "it = 14\n",
    "Fn1, Fn = Fibonacci(it)\n",
    "\n",
    "it = 14\n",
    "mu_list = np.arange(0, 5.2, 0.2)\n",
    "delta = 0.5\n",
    "\n",
    "name = 'Kitaev_SR_delta_%.2f' %delta\n",
    "\n",
    "IPR = np.load(path_data + 'IPR_%s_it_%.0f.npy'%(name,it))\n",
    "NPR = np.load(path_data + 'NPR_%s_it_%.0f.npy'%(name, it))\n",
    "evals_total = np.load(path_data + 'evals_%s_it_%.0f.npy'%(name,it))\n",
    "\n",
    "ax = fig.add_subplot(gs_plot[0:3, 0:7])\n",
    "IPR_mean =  NPR_mean = IPR_sigma = []\n",
    "\n",
    "for m, mu in enumerate(mu_list):\n",
    "\n",
    "    IPR_mean = np.append(IPR_mean, np.mean(IPR[:,m]))\n",
    "    NPR_mean = np.append(NPR_mean, np.mean(NPR[:,m]))\n",
    "    #IPR_sigma = np.append(IPR_sigma, np.sqrt(np.var(IPR[:,m])))\n",
    "\n",
    "ax.plot(mu_list, IPR_mean, 'o--', color='k', fillstyle='full', markerfacecolor='white', markeredgewidth=3, alpha=0.8, markersize=13, linewidth=3, label='MIPR')\n",
    "ax.plot(mu_list, NPR_mean, 'o--', color='k',fillstyle='full', markerfacecolor='k', markeredgewidth=1.5, alpha=0.8, markersize=13, linewidth=3, label='MNPR')   \n",
    "#ax.errorbar(mu_list, IPR_mean, yerr=IPR_sigma, color='k', alpha=0.7)\n",
    "ax.legend(fontsize=fs-15, loc=1, bbox_to_anchor=(0.95,0.65))\n",
    "#ax.set_yscale('log')\n",
    "ax.set_xlabel(r'$\\mu/t$', fontsize=fs)\n",
    "ax.set_xlim(0,4.9)\n",
    "#ax.set_ylim(0.001,1)\n",
    "\n",
    "mu_list = [0.2,1,3]\n",
    "for i, mu in enumerate(mu_list):\n",
    "    color = color_list[i]\n",
    "    ax.axvline(mu, linestyle='-', color=color, linewidth=4, alpha=0.7)\n",
    "\n",
    "ax.text(0.09, 0.6, r'$1$',\n",
    "        verticalalignment='bottom', horizontalalignment='right',\n",
    "        color = color_list[0], transform=ax.transAxes, fontsize=fs)\n",
    "ax.text(0.18, 0.85, r'$2$',\n",
    "        verticalalignment='bottom', horizontalalignment='right',\n",
    "        color = color_list[1], transform=ax.transAxes, fontsize=fs)\n",
    "ax.text(0.58, 0.75, r'$3$',\n",
    "        verticalalignment='bottom', horizontalalignment='right',\n",
    "        color = color_list[2], transform=ax.transAxes, fontsize=fs)\n",
    "    \n",
    "ax.text(-0.14, 1.05, '(a)', transform=ax.transAxes, size=40,family='STIXGeneral')\n",
    "\n",
    "############################ scaling\n",
    "\n",
    "iterations = [10,11,12,13,14,15,16,17,18,19]\n",
    "mu_list = [0.2, 1, 3]\n",
    "delta = 0.5\n",
    "it = 10\n",
    "name = 'Kitaev_SR_delta_%.2f' %delta\n",
    "\n",
    "for i, mu in enumerate(mu_list):\n",
    "\n",
    "    color = color_list[i]\n",
    "    \n",
    "    IPR_list = np.load(path_data + 'scaling_mu_%.2f_IPR_%s.npy'%(mu, name))[1:]\n",
    "    NPR_list = np.load(path_data + 'scaling_mu_%.2f_NPR_%s.npy'%(mu, name))[1:]\n",
    "    Fn_list = np.load(path_data + 'scaling_mu_%.2f_Fn_%s.npy'%(mu, name))[1:]\n",
    "    \n",
    "    ax1 = fig.add_subplot(gs_plot[i, 7:11])\n",
    "    ax1.set_yticks([])\n",
    "    ax = ax1.twinx()\n",
    "    ax.plot(1/Fn_list, IPR_list, 'o--', color=color, markerfacecolor='white', markeredgewidth=3, markersize=13, linewidth=3, label='MIPR', alpha=0.9)\n",
    "    ax.plot(1/Fn_list, NPR_list, 'o--', color=color, markerfacecolor=color, markersize=13, linewidth=3, label='MNPR', alpha=0.9)\n",
    "    ax.plot(1/Fn_list, 1/Fn_list, '--', color='k', linewidth=1, alpha=0.9)\n",
    "    ax.plot(1/Fn_list, 1/Fn_list, '--', color='k', linewidth=1, alpha=0.9)\n",
    "    \n",
    "    if i < 2:\n",
    "        ax1.set_xticks([])\n",
    "    else:\n",
    "        ax1.set_xlabel(r'$1/N$', fontsize=fs)\n",
    "        ax1.set_xticks([0, 0.01, 0.02])\n",
    "    ax.set_xlim(0,1/Fn_list[0])\n",
    "    ax.set_yscale('log')\n",
    "    ax.set_yticks([0.01, 1])\n",
    "    ax.set_ylim(0.0001, 1)\n",
    "\n",
    "    if i == 0:\n",
    "        ax.text(-0.1, 1.12, '(b)', transform=ax.transAxes, size=40,family='STIXGeneral')\n",
    "\n",
    "########################################################\n",
    "\n",
    "plt.savefig(path_figures + 'global_measures_1.pdf',bbox_inches='tight')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# FIGURE 2 - SHORT RANGE KITAEV CHAIN"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "color_list = ['lightcoral','dodgerblue','seagreen']\n",
    "marker_list = ['^-.', 'X--', 'd:']\n",
    "\n",
    "##############################################\n",
    "fig = plt.figure(figsize=(18, 16))\n",
    "\n",
    "gs_plot = gridspec.GridSpec(7, 11, figure=fig)\n",
    "gs_plot.update(wspace=0.5)\n",
    "gs_plot.update(hspace=0.05)\n",
    "\n",
    "gs_plot2 = gridspec.GridSpec(7, 22, figure=fig)\n",
    "gs_plot2.update(wspace=0.2)\n",
    "gs_plot2.update(hspace=0.2)\n",
    "\n",
    "#######################################################\n",
    "color_list = ['lightcoral','dodgerblue','seagreen']\n",
    "marker_listl = ['^-.', 'X--', 'd:']\n",
    "marker_list = ['^', 'X', 'd']\n",
    "\n",
    "gs_plot = gridspec.GridSpec(7,6, figure=fig)\n",
    "gs_plot.update(wspace=1)\n",
    "gs_plot.update(hspace=0.2)\n",
    "\n",
    "################################################\n",
    "\n",
    "ax = fig.add_subplot(gs_plot[4:7, 0:6])\n",
    "iterations = [8,9,10,11,12,13,14,15,16,17]\n",
    "\n",
    "Fn_list = []\n",
    "for it in iterations:\n",
    "    Fn_list = np.append(Fn_list, Fibonacci(it)[1])\n",
    "\n",
    "delta = 0.5\n",
    "name = 'Kitaev_SR_delta_%.2f' %delta\n",
    "mu_list = [0.2,1,3]\n",
    "\n",
    "ax.set_xlabel(r'$1/m$', fontsize = fs) \n",
    "ax.set_ylabel(r'$\\bar{\\gamma}_{\\mathrm{min}}$', fontsize = fs) \n",
    "\n",
    "for i, mu in enumerate(mu_list):\n",
    "\n",
    "    color = color_list[i]\n",
    "    marker=marker_list[i]\n",
    "    g_min = np.load(path_data + 'g_min_%s_mu_%.2f.npy' %(name,mu))\n",
    "    coef = np.polyfit(1/np.array(iterations), np.real(g_min), deg=1)\n",
    "    x = np.linspace(0,1/8)\n",
    "    ax.plot(x, coef[0]*x + coef[1], '--', color='black', linewidth=2, alpha=1)\n",
    "    ax.plot(1/np.array(iterations), np.real(g_min), marker, color=color, markersize=14, linewidth=3, alpha=0.9, label = r'$\\mu/t = %.1f$' %mu) \n",
    "    \n",
    "ax.set_xlim(0,1/iterations[0])\n",
    "ax.legend(fontsize=fs-15, loc=1, bbox_to_anchor=(0.35,0.58))\n",
    "\n",
    "ax.text(-0.1, 1.07, '(g)', transform=ax.transAxes, size=40,family='STIXGeneral')\n",
    "\n",
    "###############################################\n",
    "\n",
    "it = 10\n",
    "Fn1, Fn = Fibonacci(it)\n",
    "mu_list = [0.2, 1, 3]\n",
    "delta = 0.5\n",
    "name = 'Kitaev_SR_delta_%.2f' %delta\n",
    "heights = [0.8,0.6,0.4]\n",
    "label = ['(a)', '(b)', '(c)']\n",
    "\n",
    "for j,mu in enumerate(mu_list):\n",
    "    \n",
    "    evec = np.load(path_data + 'evecs_%s_mu_%.2f_it_%.0f.npy'%(name, mu, it))[0]\n",
    "    \n",
    "    ax = fig.add_subplot(gs_plot[j, 0:3])\n",
    "    color=color_list[j]\n",
    "    marker=marker_listl[j]\n",
    "    ax.plot(range(2*Fn), abs(evec*np.conjugate(evec)),  marker,color=color, markersize=8, linewidth=2, alpha=0.9, label = r'$\\mu = %.2f$' %mu)  \n",
    "    \n",
    "    ax.set_xlim(0,2*Fn)\n",
    "    ax.set_yticks([])    \n",
    "      \n",
    "    if j < 2:\n",
    "        ax.set_xticks([])\n",
    "    else:\n",
    "        ax.set_xticks([0,50,100,150])\n",
    "    if j == 2:\n",
    "        ax.set_xlabel(r'$j$', fontsize = fs)\n",
    "    ax.set_ylabel(r'$\\vert \\psi \\vert^2$',fontsize = fs)\n",
    "\n",
    "    ax.text(-0.17, 1, label[j], transform=ax.transAxes, size=40,family='STIXGeneral')\n",
    "        \n",
    "########################################################\n",
    "\n",
    "it = 10\n",
    "Fn1, Fn = Fibonacci(it)\n",
    "mu_list = [0.2, 1, 3]\n",
    "delta = 0.5\n",
    "name = 'Kitaev_SR_delta_%.2f' %delta\n",
    "heights = [0.8,0.6,0.4]\n",
    "label = ['(d)', '(e)', '(f)']\n",
    "for j,mu in enumerate(mu_list):\n",
    "    \n",
    "    gammas = np.load(path_data + 'spectrum_gs_%s_mu_%.2f_it_%.0f.npy' %(name, mu, it))\n",
    "    hist, bin_edges = np.histogram(gammas, 50)\n",
    "    \n",
    "    ax = fig.add_subplot(gs_plot[j, 3:6])\n",
    "    color=color_list[j]\n",
    "    marker=marker_listl[j] \n",
    "    #ax.plot(bin_edges[1:], hist, marker, color=color, markersize=8, linewidth=2, alpha=0.9, label = r'$\\mu = %.2f$' %mu) \n",
    "    ax.plot(gammas,  marker, color=color, markersize=8, linewidth=2, alpha=0.9, label = r'$\\mu = %.2f$' %mu)  \n",
    "      \n",
    "    ax.set_ylim(0,5)\n",
    "    ax.set_yticks([0,2,4])\n",
    "    if j == 2:\n",
    "        ax.set_ylim(0,20)\n",
    "        ax.set_yticks([0,10])\n",
    "    if j < 2:\n",
    "        ax.set_xticks([])\n",
    "    else:\n",
    "        ax.set_xticks([0,15,50,75])\n",
    "    ax.set_xlim(0,Fn)\n",
    "        \n",
    "    if j == 2:\n",
    "        ax.set_xlabel('$j$', fontsize = fs)\n",
    "    ax.set_ylabel(r'$\\gamma$', fontsize = fs)\n",
    "    \n",
    "    ax.text(-0.17, 1.07, label[j], transform=ax.transAxes, size=40,family='STIXGeneral')\n",
    "        \n",
    "####################################################\n",
    "\n",
    "plt.savefig(path_figures + 'global_measures_2.pdf',bbox_inches='tight')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# FIGURE 3 - SHORT RANGE KITAEV CHAIN COLOR MAP"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "color_list = ['lightcoral','dodgerblue','seagreen']\n",
    "marker_list = ['^-.', 'X--', 'd:']\n",
    "\n",
    "##############################################\n",
    "fig, ax = plt.subplots(nrows=1, ncols=1, sharex=True, sharey=False, figsize=(17,12))\n",
    "\n",
    "it = 14\n",
    "mu_list = np.arange(0, 5.2, 0.1)\n",
    "delta_list = np.arange(0, 2, 0.05)\n",
    "name = 'Kitaev_SR_map'\n",
    "Fn1, Fn = Fibonacci(it)\n",
    "\n",
    "ax.set_rasterization_zorder(5)\n",
    "\n",
    "IPR_map = np.load(path_data + 'IPR_%s_it_%.0f.npy'%(name, it))\n",
    "\n",
    "ax.set_xlabel(r'$\\mu/t$', fontsize=fs)\n",
    "ax.set_ylabel(r'$\\Delta/t$', fontsize=fs)\n",
    "ax.set_xlim(0.2,5)\n",
    "ax.set_xticks([1,2,3,4,5])\n",
    "ax.set_yticks([0,0.5,1,1.5])\n",
    "im = ax.pcolormesh(mu_list, delta_list, IPR_map, cmap='rainbow', rasterized = True)\n",
    "cbar = plt.colorbar(im, ax=ax)\n",
    "cbar.ax.set_ylabel(r'$\\bar{D}_2$', fontsize=fs)\n",
    "ax.plot(abs(delta_list+1), delta_list, 'k--', linewidth=3, alpha=0.7)\n",
    "ax.plot(abs(delta_list-1), delta_list, 'k--', linewidth=3, alpha=0.7)\n",
    "\n",
    "#######################################################\n",
    "plt.savefig(path_figures + 'global_measures_D2.pdf',bbox_inches='tight')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# FIGURE 4 - LONG RANGE MODEL WITH AHH "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "fig, axes = plt.subplots(nrows=2, ncols=2, sharex=True, sharey=False, figsize=(20,12))\n",
    "\n",
    "marker_list = ['o-', 's--', 'd:']\n",
    "cmap = 'rainbow'\n",
    "\n",
    "alpha_list = [0.5, 1.5]\n",
    "indexs = [15,10]\n",
    "\n",
    "it = 16\n",
    "Fn1, Fn = Fibonacci(it)\n",
    "\n",
    "#######################################\n",
    "mu_list = np.linspace(0, 10, 50)\n",
    "labels = ['(a)', '(b)']\n",
    "\n",
    "for j,alpha in enumerate(alpha_list):\n",
    "    \n",
    "    ax = axes[0][j]\n",
    "    ax.set_rasterization_zorder(5)\n",
    "\n",
    "    name = 'AA_nnn_%.2f' %alpha\n",
    "\n",
    "    evals_total = np.load(path_data + 'evals_ME_%s_it_%.0f.npy'%(name,it))\n",
    "    IPR_map = np.load(path_data + 'IPR_ME_%s_it_%.0f.npy'%(name,it))\n",
    "    tau_map = abs(np.log(IPR_map[::-1]))/np.log(Fn)\n",
    "\n",
    "    x = mu_list\n",
    "    for i in range(len(evals_total.T)):   \n",
    "\n",
    "        y = np.real(evals_total.T[i])\n",
    "        tau = tau_map[i]\n",
    "\n",
    "        points = np.array([x, y]).T.reshape(-1, 1, 2)\n",
    "        segments = np.concatenate([points[:-1], points[1:]], axis=1)\n",
    "\n",
    "        norm = plt.Normalize(0,1)\n",
    "        lc = LineCollection(segments, cmap='rainbow', norm=norm)\n",
    "        lc.set_array(tau)\n",
    "        lc.set_linewidth(2)\n",
    "        line = ax.add_collection(lc)\n",
    "        \n",
    "    ax.set_xlim(0,10)\n",
    "    ax.set_ylim(-10,1)\n",
    "    ax.set_xticks([])\n",
    "    if j == 0:\n",
    "        ax.set_ylabel('$E/t$', fontsize=40)\n",
    "        ax.set_yticks([-10,-5, 0])\n",
    "    else:\n",
    "        ax.set_yticks([])\n",
    "    \n",
    "    exps = [2,3,4]\n",
    "    line1 = line2 = line3 = []\n",
    "    for i,mu in enumerate(mu_list):\n",
    "        line1 = np.append(line1, evals_total[i][int((Fn1/Fn)**exps[0]*Fn)])\n",
    "        line2 = np.append(line2, evals_total[i][int((Fn1/Fn)**exps[1]*Fn)])\n",
    "        line3 = np.append(line3, evals_total[i][int((Fn1/Fn)**exps[2]*Fn)])\n",
    "\n",
    "    ax.plot(mu_list,  line1, '--', color='k', linewidth=3)\n",
    "    ax.plot(mu_list,  line2, '--', color='k', linewidth=3)\n",
    "    ax.plot(mu_list,  line3, '--', color='k', linewidth=3)\n",
    "    \n",
    "    ax.text(0.9, 0.35, r'$3$',\n",
    "            verticalalignment='bottom', horizontalalignment='right',\n",
    "            bbox={'facecolor': 'white', 'alpha': 0.7, 'pad':5},\n",
    "            color = 'k', transform=ax.transAxes, fontsize=fs)\n",
    "    ax.text(0.8, 0.25, r'$2$',\n",
    "            verticalalignment='bottom', horizontalalignment='right',\n",
    "            bbox={'facecolor': 'white', 'alpha': 0.7, 'pad': 5},\n",
    "            color = 'k', transform=ax.transAxes, fontsize=fs)\n",
    "    ax.text(0.7, 0.1, r'$1$',\n",
    "            verticalalignment='bottom', horizontalalignment='right',\n",
    "            bbox={'facecolor': 'white', 'alpha': 0.7, 'pad': 5},\n",
    "            color = 'k', transform=ax.transAxes, fontsize=fs)\n",
    "    \n",
    "    #ax.axvline(mu_list[indexs[j]], linestyle = '--', color='r', linewidth=2, alpha = 0.7)\n",
    "    \n",
    "    if j == 0:\n",
    "        ax.text(-0.25, 0.97, labels[j], transform=ax.transAxes, size=40, family='STIXGeneral')    \n",
    "    else:\n",
    "        ax.text(-0.15, 0.97, labels[j], transform=ax.transAxes, size=40, family='STIXGeneral')    \n",
    "    \n",
    "######################################################\n",
    "mu_list = np.linspace(0, 10, 50)\n",
    "alpha_list = [0.5,1.5]\n",
    "exps = [2,3,4]\n",
    "labels = ['(c)', '(d)']\n",
    "color_list = ['lightcoral','dodgerblue','seagreen']\n",
    "markers = ['o-', 's--', 'd:']\n",
    "labels_plot = [r'$n/L \\leq \\beta^2$', r'$\\beta^2 \\leq  n/L \\leq \\beta^3$', r'$\\beta^3 \\leq n/L \\leq \\beta^4$']\n",
    "for i, alpha in enumerate(alpha_list):\n",
    "\n",
    "    ax = axes[1][i]\n",
    "    name = 'AA_nnn_%.2f' %alpha\n",
    "    IPR_map = np.load(path_data + 'IPR_ME_%s_it_%.0f.npy'%(name,it))\n",
    "    D2_map = abs(np.log(IPR_map[::-1]))/np.log(Fn)\n",
    "\n",
    "    for j,exp in enumerate(exps):\n",
    "        color = color_list[j]\n",
    "        D2_mean = D2_sigma = []\n",
    "        for D2 in D2_map.T:   \n",
    "            band_max = (Fn1/Fn)**(exp-1)\n",
    "            band_min = (Fn1/Fn)**exp\n",
    "            nL = np.arange(Fn)/Fn\n",
    "            D2_band = D2[(nL<band_max)&(nL>band_min)]\n",
    "            D2_mean = np.append(D2_mean, np.mean(D2_band))\n",
    "            D2_sigma = np.append(D2_sigma, np.sqrt(np.var(D2_band)))\n",
    "\n",
    "        ax.plot(mu_list[::2], D2_mean[::2], markers[j], color=color, linewidth=3, markersize=10, alpha=0.7, label=labels_plot[j])\n",
    "        #ax.fill_between(mu_list[::2], D2_mean[::2] - D2_sigma[::2], D2_mean[::2] + D2_sigma[::2], color=color, alpha=0.7)\n",
    "\n",
    "        if i == 0:\n",
    "            ax.set_yticks([0,0.25,0.5,0.75])\n",
    "            ax.set_ylabel(r'$\\bar{D}_2$', fontsize=fs)\n",
    "        else:\n",
    "            ax.set_yticks([])\n",
    "        \n",
    "        ax.set_xticks([0,2,4,6,8,10])\n",
    "        ax.set_ylim(0,1)\n",
    "        ax.set_xlim(0,10)\n",
    "        ax.set_xlabel(r'$\\mu/t$', fontsize=fs)\n",
    "        ax.legend(fontsize=fs-20)\n",
    "        \n",
    "    if i == 0:\n",
    "        ax.text(-0.25, 0.97, labels[i], transform=ax.transAxes, size=40, family='STIXGeneral')    \n",
    "    else:\n",
    "        ax.text(-0.15, 0.97, labels[i], transform=ax.transAxes, size=40, family='STIXGeneral')    \n",
    "    \n",
    "\n",
    "######################################################\n",
    "plt.tight_layout()\n",
    "cbar = plt.colorbar(lc, ax=axes.ravel().tolist())\n",
    "cbar.ax.set_ylabel(r'$D_2$', fontsize=fs)        \n",
    "##########################################\n",
    "fig.savefig(path_figures + 'local_measures.pdf',bbox_inches='tight')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# FIGURE 5 - LONG RANGE MODEL WITH AHH ENERGIES"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "mu_list = np.linspace(0, 10, 100)[1:]\n",
    "\n",
    "it = 18\n",
    "Fn1, Fn = Fibonacci(it)\n",
    "\n",
    "fig, axes = plt.subplots(nrows=1, ncols=2, sharex=True, sharey=True, figsize=(17,7))\n",
    "\n",
    "cmap = 'rainbow'\n",
    "color_list = ['lightcoral','seagreen']\n",
    "\n",
    "alpha_list = [0.5, 1.5]\n",
    "mu = 2\n",
    "\n",
    "#########################################\n",
    "mu_list = np.linspace(0, 5, 50)\n",
    "\n",
    "labels = ['(a)', '(b)']\n",
    "\n",
    "for i,alpha in enumerate(alpha_list):\n",
    "\n",
    "    ax =  axes[i]\n",
    "    ax.set_rasterization_zorder(5)\n",
    "    \n",
    "    name = 'AA_nnn_%.2f' %alpha\n",
    "    evals_list = np.load(path_data + 'evals_ME_%s_it_%.0f_mu_%.2f.npy'%(name,it,mu))\n",
    "\n",
    "    odd_diff = even_diff = []\n",
    "\n",
    "    for j in range(1,int(len(evals_list)/2)):\n",
    "\n",
    "        odd_diff = np.append(odd_diff, evals_list[2*j]-evals_list[2*j-1])\n",
    "        even_diff = np.append(even_diff, evals_list[2*j+1]-evals_list[2*j])\n",
    "\n",
    "    ax.plot(np.arange(len(odd_diff))[::-1]/len(odd_diff), np.log(odd_diff), 'v', color=color_list[1], markersize= 4, alpha=0.7, label=r'log($S_n^{o-e}$)')\n",
    "    ax.plot(np.arange(len(even_diff))[::-1]/len(even_diff), np.log(even_diff), 'X', color=color_list[0], markersize = 4, alpha=0.7, label=r'log($S_n^{e-o}$)')\n",
    "    ax.axvline(Fn1/Fn, color='k', linestyle='--', linewidth=3, alpha=0.7)\n",
    "    ax.axvline((Fn1/Fn)**2, color='k', linestyle='--', linewidth=3, alpha=0.7)\n",
    "    ax.axvline((Fn1/Fn)**3, color='k', linestyle='--', linewidth=3, alpha=0.7)\n",
    "    ax.axvline((Fn1/Fn)**4, color='k', linestyle='--', linewidth=3, alpha=0.7)\n",
    "    #ax.axvline(1-(Fn1/Fn)**5, color='k', linestyle='--', linewidth=3, alpha=0.7)\n",
    "    ax.set_yticks([0,-10,-20,-30])\n",
    "    \n",
    "    if i == 0:\n",
    "        ax.text(0.35, 0.05, r'$\\beta^3$',\n",
    "        verticalalignment='bottom', horizontalalignment='right',\n",
    "        color = 'k', transform=ax.transAxes, fontsize=fs-5)\n",
    "    else:\n",
    "        ax.text(0.5, 0.05, r'$\\beta^2$',\n",
    "        verticalalignment='bottom', horizontalalignment='right',\n",
    "        color = 'k', transform=ax.transAxes, fontsize=fs-5)\n",
    "        \n",
    "    if i == 0:\n",
    "        ax.legend(fontsize=fs-15, markerscale=1.5, loc=1, bbox_to_anchor=(0.99,0.6))\n",
    "    ax.set_xlabel(r'$n/N$', fontsize=fs) \n",
    "    ax.set_xlim(0,1)\n",
    "    \n",
    "    ax.text(0.92, 0.07, r'$\\xi = %.1f \\\\ \\mu/t = %.1f$' %(alpha, mu),\n",
    "        verticalalignment='bottom', horizontalalignment='right',\n",
    "        bbox={'facecolor': 'white', 'edgecolor': 'white', 'alpha': 1, 'pad': 5},\n",
    "        color = 'k', transform=ax.transAxes, fontsize=fs-10)\n",
    "    \n",
    "    ax.text(-0.18, 0.97, labels[i], transform=ax.transAxes, size=40, family='STIXGeneral')    \n",
    "    \n",
    "######################################################\n",
    "fig.savefig(path_figures + 'els_delta_0.pdf',bbox_inches='tight')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# FIGURE 6 - COLOR MAPS FOR LONG RANGE KITAEV CHAIN WITH AAH"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "it = 14\n",
    "Fn1, Fn = Fibonacci(it)\n",
    "\n",
    "fig, axes = plt.subplots(nrows=2, ncols=3, sharex=False, sharey=False, figsize=(20,12))\n",
    "cmap = 'rainbow'\n",
    "    \n",
    "#########################################################\n",
    "\n",
    "mu_list = np.linspace(0, 10, 100)[1:]\n",
    "alpha_list = np.arange(0, 3.1, 0.05)\n",
    "delta_list = [0.1, 0.5, 1]\n",
    "\n",
    "tau_min=1\n",
    "tau_max=0\n",
    "\n",
    "for i,delta in enumerate(delta_list):\n",
    "\n",
    "    name = 'LR_alpha_%.2f_delta_%.2f' %(alpha, delta)\n",
    "    tau_map = np.load(path_data + 'IPR_ME_%s_it_%.0f.npy'%(name, it))\n",
    "        \n",
    "    for tau in tau_map:\n",
    "        if tau.min()<tau_min:\n",
    "            tau_min = tau.min()\n",
    "        if tau.max()>tau_max:\n",
    "            tau_max = tau.max()\n",
    "            \n",
    "for i,alpha in enumerate(alpha_list):\n",
    "\n",
    "    name = 'LR_alpha_%.2f_delta_%.2f' %(alpha, delta)\n",
    "    tau_map = np.load(path_data + 'IPR_ME_%s_it_%.0f.npy'%(name, it))\n",
    "    \n",
    "    for tau in tau_map:\n",
    "        if tau.min()<tau_min:\n",
    "            tau_min = tau.min()\n",
    "        if tau.max()>tau_max:\n",
    "            tau_max = tau.max()\n",
    "            \n",
    "norm = colors.Normalize(vmin=tau_min, vmax=tau_max)\n",
    "\n",
    "for i,delta in enumerate(delta_list):\n",
    "\n",
    "    ax = axes[1][i]\n",
    "    ax.set_rasterization_zorder(0)\n",
    "    \n",
    "    mean = []\n",
    "    alpha_list = np.arange(0, 3.1, 0.05)\n",
    "    for alpha in alpha_list:        \n",
    "        \n",
    "        name = 'LR_alpha_%.2f_delta_%.2f' %(alpha, delta)\n",
    "\n",
    "        IPR_map = np.load(path_data + 'IPR_ME_%s_it_%.0f.npy'%(name, it))\n",
    "        IPR_map = abs(np.log(IPR_map[::-1]))/np.log(Fn)\n",
    "        evals_total = np.load(path_data + 'evals_ME_%s_it_%.0f.npy'%(name, it))\n",
    "        if len(mean) == 0:\n",
    "            mean = np.mean(IPR_map, axis=0)\n",
    "        else:\n",
    "            mean = np.vstack((mean, np.mean(IPR_map, axis=0)))\n",
    "\n",
    "    im = ax.pcolormesh(mu_list, alpha_list, mean, norm=norm, cmap=cmap, rasterized = True)\n",
    "    ax.axhline(1, color='k', linestyle='--', linewidth=3, alpha=0.7)\n",
    "    ax.axvline(abs(delta+1), color='k', linestyle='--', linewidth=3, alpha=0.7)\n",
    "    ax.axvline(abs(delta-1), color='k', linestyle='--', linewidth=3, alpha=0.7)\n",
    "    \n",
    "    ax.set_xlim(0.1,7.5)\n",
    "    ax.set_ylim(0.1, 3)\n",
    "    if i > 0:\n",
    "        ax.set_yticks([])\n",
    "    else:\n",
    "        ax.set_yticks([0.5, 1, 1.5, 2, 2.5])\n",
    "        ax.set_ylabel(r'$\\alpha$', fontsize=fs)\n",
    "\n",
    "    ax.set_xlabel(r'$\\mu/t$', fontsize=fs)\n",
    "    #ax.set_xlabel(r'$\\mu/t$', fontsize=fs)\n",
    "    ax.text(0.9, 0.8, r'$\\Delta/t = %.2f$' %delta,\n",
    "            verticalalignment='bottom', horizontalalignment='right',\n",
    "            color = 'k', transform=ax.transAxes, fontsize=fs)\n",
    "\n",
    "##########################################################\n",
    "mu_list = np.linspace(0, 10, 100)[1:]\n",
    "delta_list = np.arange(0, 2.1, 0.05)\n",
    "alpha_list = [5, 2, 0.5]\n",
    "        \n",
    "for i,alpha in enumerate(alpha_list):\n",
    "\n",
    "    ax = axes[0][i]\n",
    "    ax.set_rasterization_zorder(0)\n",
    "    \n",
    "    mean = []\n",
    "    delta_list = np.arange(0, 2.1, 0.05)\n",
    "    for delta in delta_list:\n",
    "\n",
    "        name = 'LR_alpha_%.2f_delta_%.2f' %(alpha, delta)\n",
    "\n",
    "        IPR_map = np.load(path_data + 'IPR_ME_%s_it_%.0f.npy'%(name, it))\n",
    "        IPR_map = abs(np.log(IPR_map[::-1]))/np.log(Fn)\n",
    "        evals_total = np.load(path_data + 'evals_ME_%s_it_%.0f.npy'%(name, it))\n",
    "        if len(mean) == 0:\n",
    "            mean = np.mean(IPR_map, axis=0)\n",
    "        else:\n",
    "            mean = np.vstack((mean, np.mean(IPR_map, axis=0)))\n",
    "\n",
    "    im = ax.pcolormesh(mu_list, delta_list, mean, norm=norm, cmap=cmap, rasterized = True)\n",
    "    ax.plot(abs(delta_list+1), delta_list, 'k--', linewidth=3, alpha=0.7)\n",
    "    ax.plot(abs(delta_list-1), delta_list, 'k--', linewidth=3, alpha=0.7)\n",
    "    \n",
    "    if i > 0:\n",
    "        ax.set_yticks([])\n",
    "    else:\n",
    "        ax.set_ylabel(r'$\\Delta/t$', fontsize=fs)\n",
    "        ax.set_yticks([0.5,1,1.5,2])\n",
    "\n",
    "    #ax.set_xticks([1,2,3,4,5])\n",
    "    ax.set_xlim(0.1,7.5)\n",
    "    ax.set_ylim(0,2)\n",
    "    \n",
    "    ax.set_xticks([])\n",
    "    ax.text(0.9, 0.1, r'$\\alpha = %.2f$' %alpha,\n",
    "            verticalalignment='bottom', horizontalalignment='right',\n",
    "            color = 'k', transform=ax.transAxes, fontsize=fs)\n",
    "    \n",
    "#################################################################\n",
    "plt.tight_layout()\n",
    "cbar = plt.colorbar(im, ax=axes.ravel().tolist())\n",
    "cbar.ax.set_ylabel(r'$\\bar{D}_2$', fontsize=fs)\n",
    "\n",
    "labels = ['(a)','(b)','(c)','(d)','(e)','(f)']\n",
    "for ax,label in zip(axes.flat, labels):\n",
    "    ax.text(0.02, 0.9, label, bbox={'facecolor': 'white', 'edgecolor': 'white', 'alpha': 0.8, 'pad':1}, transform=ax.transAxes, size=40,family='STIXGeneral')\n",
    "\n",
    "#######################################################\n",
    "fig.savefig(path_figures + 'phase_diagram.pdf',bbox_inches='tight')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# FIGURE 7 - CUT BANDS FOR LONG RANGE KITAEV CHAIN WITH AAH"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "mu_list = np.linspace(0, 10, 100)[1:]\n",
    "alpha_list = [0.5,2,5]\n",
    "delta = 0.8\n",
    "idx = 20\n",
    "\n",
    "it = 18\n",
    "Fn1, Fn = Fibonacci(it)\n",
    "\n",
    "fig = plt.figure(figsize=(30, 20))\n",
    "\n",
    "gs_plot = gridspec.GridSpec(7, 3, figure=fig)\n",
    "gs_plot.update(hspace=0.05)\n",
    "axes_list = []\n",
    "\n",
    "cmap = 'rainbow'\n",
    "\n",
    "nums_i = [[0,0.8], [0.8, 1.8],[1.8, 3]]\n",
    "nums_0 = [[0,1], [1, 1.4],[1.4, 1.8]]\n",
    "position_y = [[0.07, 0.35, 0.54, 0.73],[0.05, 0.4, 0.62, 0.8],[0.05, 0.4, 0.62,0.8]]\n",
    "\n",
    "tau_min=1\n",
    "tau_max=0\n",
    "    \n",
    "labels = ['(a)', '(b)', '(c)']\n",
    "##################################################33\n",
    "for ja,alpha in enumerate(alpha_list):\n",
    "\n",
    "    ax = fig.add_subplot(gs_plot[0:3, ja])\n",
    "    axes_list = np.append(axes_list, ax)\n",
    "    ax.set_rasterization_zorder(0)\n",
    "\n",
    "    name = 'LR_alpha_%.2f_delta_%.2f' %(alpha, delta)\n",
    "    IPR_map = np.load(path_data + 'IPR_ME_%s_it_%.0f.npy'%(name, it))\n",
    "    tau_map = abs(np.log(IPR_map[::-1]))/np.log(Fn)\n",
    "    evals_total = np.load(path_data + 'evals_ME_%s_it_%.0f.npy'%(name, it))\n",
    "    \n",
    "    for tau in tau_map:\n",
    "        if tau.min()<tau_min:\n",
    "            tau_min = tau.min()\n",
    "        if tau.max()>tau_max:\n",
    "            tau_max = tau.max()\n",
    "            \n",
    "    x = mu_list\n",
    "    for i in range(len(evals_total.T)):   \n",
    "\n",
    "        y = np.real(evals_total.T[i])\n",
    "        tau = tau_map[i]\n",
    "\n",
    "        points = np.array([x, y]).T.reshape(-1, 1, 2)\n",
    "        segments = np.concatenate([points[:-1], points[1:]], axis=1)\n",
    "\n",
    "        norm = colors.Normalize(vmin=tau_min, vmax=tau_max)\n",
    "        lc = LineCollection(segments, cmap=cmap, norm=norm, zorder=-1)\n",
    "        lc.set_array(tau)\n",
    "        lc.set_linewidth(2)\n",
    "        line = ax.add_collection(lc)\n",
    "        \n",
    "    if ja == 0:\n",
    "        nums = nums_0\n",
    "    else:\n",
    "        nums = nums_i\n",
    "    \n",
    "    evals_m = evals_total[idx]\n",
    "    for j,num in enumerate(nums):\n",
    "        linemax=[]\n",
    "        for i,mu in enumerate(mu_list):\n",
    "            \n",
    "            evals = evals_total[i]\n",
    "            evals_range = evals[(evals_m < num[1])&(evals_m > num[0])]\n",
    "            linemax = np.append(linemax, evals_range[-1])\n",
    "            \n",
    "        ax.plot(mu_list,  linemax, '--', color='k', linewidth=3)\n",
    "    \n",
    "    ax.text(0.9, position_y[ja][0], r'$1$',\n",
    "            verticalalignment='bottom', horizontalalignment='right',\n",
    "            bbox={'facecolor': 'white', 'alpha': 0.7, 'pad':5},\n",
    "            color = 'k', transform=ax.transAxes, fontsize=fs)\n",
    "    ax.text(0.9, position_y[ja][1], r'$2$',\n",
    "            verticalalignment='bottom', horizontalalignment='right',\n",
    "            bbox={'facecolor': 'white', 'alpha': 0.7, 'pad': 5},\n",
    "            color = 'k', transform=ax.transAxes, fontsize=fs)\n",
    "    ax.text(0.9, position_y[ja][2], r'$3$',\n",
    "            verticalalignment='bottom', horizontalalignment='right',\n",
    "            bbox={'facecolor': 'white', 'alpha': 0.7, 'pad': 5},\n",
    "            color = 'k', transform=ax.transAxes, fontsize=fs)\n",
    "    #ax.text(0.9, position_y[ja][3], r'$4$',\n",
    "    #        verticalalignment='bottom', horizontalalignment='right',\n",
    "    #        bbox={'facecolor': 'white', 'alpha': 0.7, 'pad': 5},\n",
    "    #        color = 'k', transform=ax.transAxes, fontsize=fs)\n",
    "    \n",
    "    ax.set_ylim(0,10)\n",
    "    ax.set_xlim(0.1,10)\n",
    "    ax.set_xticks([])\n",
    "    \n",
    "    if ja == 0:\n",
    "        ax.set_ylabel(r'$E/t$', fontsize=fs)\n",
    "        ax.set_yticks([0,3,6,9])\n",
    "    else:\n",
    "        ax.set_yticks([])\n",
    "        \n",
    "    ax.text(0.02, 0.9, labels[ja], bbox={'facecolor': 'white', 'edgecolor': \n",
    "                                    'white', 'alpha': 0.8, 'pad':1}, transform=ax.transAxes, size=40,family='STIXGeneral')  \n",
    "\n",
    "#############################################\n",
    "\n",
    "cmap = 'rainbow'\n",
    "\n",
    "nums_i = [[0,0.8], [0.8, 1.8],[1.8, 3]]\n",
    "nums_0 = [[0,1], [1, 1.4],[1.4, 1.8]]\n",
    "position_y = [[0.07, 0.35, 0.54, 0.73],[0.05, 0.4, 0.62, 0.8],[0.05, 0.4, 0.62,0.8]]\n",
    "\n",
    "color_list = ['lightcoral','dodgerblue','seagreen','goldenrod']\n",
    "markers = ['o-', 's--', 'd:', '*-.']\n",
    "labels = np.array([['(d)', '(e)', '(f)'],['(g)', '(h)', '(i)'],['(j)', '(k)', '(l)']]).T\n",
    "\n",
    "\n",
    "for i, alpha in enumerate(alpha_list):\n",
    "\n",
    "    if i == 0:\n",
    "        nums = nums_0\n",
    "    else:\n",
    "        nums = nums_i\n",
    "        \n",
    "    for j,num in enumerate(nums):\n",
    "        \n",
    "        ax = fig.add_subplot(gs_plot[j+3, i])\n",
    "        axes_list = np.append(axes_list, ax)\n",
    "        \n",
    "        ax.set_rasterization_zorder(0)\n",
    "    \n",
    "        color = color_list[j]\n",
    "        \n",
    "        name = 'LR_alpha_%.2f_delta_%.2f' %(alpha, delta)\n",
    "        IPR_map = np.load(path_data + 'IPR_ME_%s_it_%.0f.npy'%(name, it))\n",
    "        D2_map = abs(np.log(IPR_map[::-1]))/np.log(Fn)\n",
    "        evals_total = np.load(path_data + 'evals_ME_%s_it_%.0f.npy'%(name, it))\n",
    "        \n",
    "        D2_mean = D2_sigma = []\n",
    "        evals_m = evals_total[idx]\n",
    "        for D2 in D2_map.T:   \n",
    "            D2_mean = np.append(D2_mean, np.mean(D2[(abs(evals_m) < num[1])&(abs(evals_m) > num[0])]))\n",
    "            D2_sigma = np.append(D2_sigma, np.sqrt(np.var(D2[(abs(evals_m) < num[1])&(abs(evals_m) > num[0])])))\n",
    "            \n",
    "        ax.plot(mu_list[::2], D2_mean[::2], markers[j], color=color, linewidth=3, markersize=8, alpha=1, label=r'$i=%.0f$' %(j+1))\n",
    "        #ax.errorbar(mu_list[::1], D2_mean[::1], yerr=D2_sigma[::1], color='k', alpha=0.7)\n",
    "        ax.fill_between(mu_list, D2_mean-D2_sigma, D2_mean+D2_sigma, color='k', alpha=0.3)\n",
    "        \n",
    "        ax.set_ylim(0,1.05)\n",
    "        if i == 0:\n",
    "            ax.set_ylabel(r'$\\bar{D}_2^i$', fontsize=fs)\n",
    "            ax.set_yticks([0, 0.5])\n",
    "        else:\n",
    "            ax.set_yticks([])\n",
    "        \n",
    "        if j == 2:\n",
    "            ax.set_xlabel(r'$\\mu/t$', fontsize=fs)\n",
    "            ax.set_xticks([0,5,10])\n",
    "        else:\n",
    "            ax.set_xticks([])\n",
    "            \n",
    "        if i == 2:\n",
    "            ax.legend(fontsize=fs-15)\n",
    "            \n",
    "        ax.text(0.02, 0.1, labels[i][j], transform=ax.transAxes, size=35,family='STIXGeneral')\n",
    "             \n",
    "######################################################\n",
    "\n",
    "cbar = plt.colorbar(lc, ax=axes_list, fraction=0.1)\n",
    "cbar.ax.set_ylabel(r'$D_2$', fontsize=fs)\n",
    "\n",
    "plt.tight_layout()\n",
    "    \n",
    "######################################################\n",
    "fig.savefig(path_figures + 'bands.pdf',bbox_inches='tight')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# FIGURE 8 - ENERGY LEVEL SPACING"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "mu_list = np.linspace(0, 10, 100)[1:]\n",
    "delta = 0.8\n",
    "\n",
    "it = 18\n",
    "Fn1, Fn = Fibonacci(it)\n",
    "\n",
    "fig = plt.figure(figsize=(20, 18))\n",
    "\n",
    "gs_plot = gridspec.GridSpec(12, 1, figure=fig)\n",
    "#gs_plot.update(wspace=0.5)\n",
    "gs_plot.update(hspace=0)\n",
    "\n",
    "cmap = 'rainbow'\n",
    "color_list = ['lightcoral','seagreen', 'lightcoral']\n",
    "        \n",
    "alpha_list = [0.5,2, 5]\n",
    "mu_list = [2, 2, 2]\n",
    "\n",
    "labels = ['(a)', '(b)', '(c)']\n",
    "labels_data = [r'log($S_n^{o-e}$)', r'log($S_n^{e-o}$)', r'log($S_n^{o-e}$)']\n",
    "markers = ['v', 'X', 'v']\n",
    "\n",
    "ja = 0\n",
    "for i,alpha in enumerate(alpha_list):\n",
    "\n",
    "    ax = fig.add_subplot(gs_plot[2*ja:2*ja+2, 0])\n",
    "    ax.set_rasterization_zorder(5)\n",
    "    \n",
    "    mu = mu_list[i]\n",
    "    \n",
    "    name = 'LR_alpha_%.2f_delta_%.2f' %(alpha, delta)\n",
    "    evals_list = np.load(path_data + 'evals_ME_%s_it_%.0f_mu_%.2f.npy'%(name, it, mu))\n",
    "    IPR_list = np.load(path_data + 'IPR_ME_%s_it_%.0f_mu_%.0f.npy'%(name, it, mu))\n",
    "    #NPR_list = np.load(path_data + 'NPR_ME_%s_it_%.0f_mu_%.0f.npy'%(name, it, mu))\n",
    "    \n",
    "    IPR_list = IPR_list[evals_list>0]\n",
    "    evals_list = evals_list[evals_list>0]\n",
    "    odd_diff = even_diff = []\n",
    "\n",
    "    for j in range(1,int(len(evals_list)/2)):\n",
    "\n",
    "        odd_diff = np.append(odd_diff, evals_list[2*j]-evals_list[2*j-1])\n",
    "        even_diff = np.append(even_diff, evals_list[2*j+1]-evals_list[2*j])\n",
    "\n",
    "    ax.plot(np.arange(len(odd_diff))[::-1]/len(odd_diff), np.log(odd_diff)[::-1], markers[abs(i-1)], color=color_list[abs(i-1)], markersize= 4, alpha=0.7, label=labels_data[abs(i-1)])\n",
    "    ax.plot(np.arange(len(even_diff))[::-1]/len(even_diff), np.log(even_diff)[::-1],markers[i], color=color_list[i], markersize = 4, alpha=0.7, label=labels_data[i])\n",
    "    #ax1 = ax.twinx()\n",
    "    #ax1.plot(np.arange(len(even_diff))/len(even_diff), abs(np.log(IPR_list[::2][2:]))/np.log(Fn),'o-', color='tab:blue', markersize = 4, alpha=0.7, label='IPR')\n",
    "    ax.axvline(1-Fn1/Fn, color='k', linestyle='--', linewidth=3, alpha=1)\n",
    "    ax.axvline(1-(Fn1/Fn)**2, color='k', linestyle='--', linewidth=3, alpha=1)\n",
    "    ax.axvline(1-(Fn1/Fn)**3, color='k', linestyle='--', linewidth=3, alpha=1)\n",
    "    ax.axvline(1-(Fn1/Fn)**4, color='k', linestyle='--', linewidth=3, alpha=1)\n",
    "    ax.axvline(1-(Fn1/Fn)**5, color='k', linestyle='--', linewidth=3, alpha=1)\n",
    "\n",
    "    ax1 = fig.add_subplot(gs_plot[2*ja+2:2*ja+3, 0])\n",
    "    evals_list = evals_list[::-1]\n",
    "    ax1.plot(np.arange(len(evals_list))/len(evals_list), evals_list[::-1], 'k-', linewidth= 3, alpha=1, label=labels_data[abs(i-1)])\n",
    "    if i==0:\n",
    "        ax1.set_ylim(-0.1,5.5)\n",
    "        ax1.set_yticks([2.5,5])\n",
    "    if i==1:\n",
    "        ax1.set_ylim(-0.1,3.5)\n",
    "        ax1.set_yticks([1,3])\n",
    "    if i==2:\n",
    "        ax1.set_ylim(-0.1,3.5)\n",
    "        ax1.set_yticks([1,3])\n",
    "        \n",
    "    ax1.set_xlim(0,1)\n",
    "    ax1.set_ylabel(r'$E/t$', fontsize=fs) \n",
    "    \n",
    "    ax.set_yticks([0,-10,-20,-30])\n",
    "    ax.set_xticks([])\n",
    "    ax.set_xlim(0,1)\n",
    "    if i == 2:\n",
    "        ax1.set_xlabel(r'$n/N$', fontsize=fs) \n",
    "    if i == 1:\n",
    "        ax.legend(fontsize=fs-15, markerscale=3, loc=1, bbox_to_anchor=(0.8,0.65))\n",
    "        \n",
    "    #ax.text(0.97, 0.05, r'$    \\alpha = %.1f \\\\ \\mu/t = %.1f$' %(alpha, mu),\n",
    "    #    verticalalignment='bottom', horizontalalignment='right',\n",
    "    #    bbox={'facecolor': 'white', 'edgecolor': 'white', 'alpha': 0.5, 'pad': 5},\n",
    "    #    color = 'k', transform=ax.transAxes, fontsize=fs-10)\n",
    "    \n",
    "    ax.text(-0.08, 0.97, labels[i],transform= ax.transAxes, size=40,family='STIXGeneral')\n",
    "    \n",
    "    ja += 2\n",
    "######################################################\n",
    "fig.savefig(path_figures + 'els.pdf',bbox_inches='tight')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# FIGURE 9 - HISTOGRAM"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "iterations = np.array([15,16,17,18,19])\n",
    "mu = 2\n",
    "alpha = 5\n",
    "delta = 0.8\n",
    "L = 1\n",
    "\n",
    "Fn_list = []\n",
    "\n",
    "IPR_mean1 = IPR_mean2 = IPR_mean3 = IPR_mean4 = []\n",
    "fig, axes = plt.subplots(nrows=1, ncols=2, sharex=False, sharey=False, figsize=(15, 7,))\n",
    "\n",
    "color_list = ['lightcoral','dodgerblue','seagreen','goldenrod']\n",
    "markers = ['o', 'd', 's', '*']\n",
    "for it in iterations:\n",
    "    \n",
    "    name = 'LR_alpha_%.2f_delta_%.2f' %(alpha, delta)\n",
    "\n",
    "    Fn1, Fn = Fibonacci(it)\n",
    "    Fn_list = np.append(Fn_list, Fn)\n",
    "    length = 1\n",
    "\n",
    "    IPR = np.load(path_data + 'IPR_ME_%s_it_%.0f_mu_%.0f.npy'%(name, it, mu))\n",
    "    evals = np.load(path_data + 'evals_ME_%s_it_%.0f_mu_%.0f.npy'%(name, it, mu))\n",
    "\n",
    "    IPR = IPR[evals>0]\n",
    "    evals = evals[evals>0]\n",
    "    \n",
    "    IPR_new = IPR    \n",
    "    \n",
    "    IPR_new1 = abs(np.log(IPR_new[Fn1-int(0.09*Fn):Fn1])/np.log(Fn))\n",
    "    IPR_mean1 = np.append(IPR_mean1, np.mean(IPR_new1))\n",
    "    \n",
    "    IPR_new2 = abs(np.log(IPR_new[0:Fn1-int(0.09*Fn)])/np.log(Fn))\n",
    "    IPR_mean2 = np.append(IPR_mean2, np.mean(IPR_new2))\n",
    "    \n",
    "    IPR_new3 = abs(np.log(IPR_new[Fn1:Fn1+int(0.146*Fn)])/np.log(Fn))\n",
    "    IPR_mean3 = np.append(IPR_mean3, np.mean(IPR_new3))\n",
    "    \n",
    "    IPR_new4 = abs(np.log(IPR_new[Fn1+int(0.146*Fn):])/np.log(Fn))\n",
    "    IPR_mean4 = np.append(IPR_mean4, np.mean(IPR_new4))\n",
    "\n",
    "    if it == 19:\n",
    "        ax = axes[0]\n",
    "        ax.plot(np.arange(Fn)[Fn1-int(0.09*Fn):Fn1]/Fn, IPR_new1, '.', color=color_list[0], linewidth=2)\n",
    "        ax.plot(np.arange(Fn)[0:Fn1-int(0.09*Fn)]/Fn, IPR_new2, '.', color=color_list[1], linewidth=2)\n",
    "        ax.plot(np.arange(Fn)[Fn1:Fn1+int(0.146*Fn)]/Fn, IPR_new3, '.', color=color_list[2], linewidth=2)\n",
    "        ax.plot(np.arange(Fn)[Fn1+int(0.146*Fn):]/Fn, IPR_new4, '.', color=color_list[3], linewidth=2)\n",
    "        ax.axvline(Fn1/Fn, color='k', linestyle='--', linewidth=3, alpha=1)\n",
    "        ax.axvline((Fn1-int(0.09*Fn))/Fn, color='k', linestyle='--', linewidth=3, alpha=1)    \n",
    "        ax.axvline((Fn1+int(0.145*Fn))/Fn, color='k', linestyle='--', linewidth=3, alpha=1)   \n",
    "        ax.set_xlim((Fn1-int(0.35*Fn))/Fn, (Fn-int(0.05*Fn))/Fn)\n",
    "        \n",
    "        ax.set_ylim(0,1)\n",
    "        ax.set_xlabel(r'$n/N$', fontsize=fs)\n",
    "        ax.set_ylabel(r'$D_2$', fontsize=fs)\n",
    "        \n",
    "        ax.text(0.1, 0.2, r'$1$',\n",
    "            verticalalignment='bottom', horizontalalignment='right',\n",
    "            bbox={'facecolor': 'white', 'alpha': 0.7, 'pad':5},\n",
    "            color = 'k', transform=ax.transAxes, fontsize=fs)\n",
    "        ax.text(0.46, 0.3, r'$2$',\n",
    "            verticalalignment='bottom', horizontalalignment='right',\n",
    "            bbox={'facecolor': 'white', 'alpha': 0.7, 'pad': 5},\n",
    "            color = 'k', transform=ax.transAxes, fontsize=fs)\n",
    "        ax.text(0.6, 0.7, r'$3$',\n",
    "            verticalalignment='bottom', horizontalalignment='right',\n",
    "            bbox={'facecolor': 'white', 'alpha': 0.7, 'pad': 5},\n",
    "            color = 'k', transform=ax.transAxes, fontsize=fs)\n",
    "        ax.text(0.9, 0.5, r'$4$',\n",
    "            verticalalignment='bottom', horizontalalignment='right',\n",
    "            bbox={'facecolor': 'white', 'alpha': 0.7, 'pad': 5},\n",
    "            color = 'k', transform=ax.transAxes, fontsize=fs)\n",
    "        \n",
    "        ax.text(-0.3, 0.97, '(a)' ,transform= ax.transAxes, size=40,family='STIXGeneral')\n",
    "        \n",
    "        ax = axes[1]\n",
    "        ax.set_yticks([])\n",
    "        ax.set_xlabel(r'$D_2$', fontsize=fs)        \n",
    "        ax = ax.twinx()\n",
    "\n",
    "        bins= 50\n",
    "        hist1, bin_edges1 = np.histogram(IPR_new1, bins=bins, normed=True)\n",
    "        hist2, bin_edges2 = np.histogram(IPR_new2, bins=bins, normed=True)\n",
    "        hist3, bin_edges3 = np.histogram(IPR_new3, bins=bins, normed=True)\n",
    "        hist4, bin_edges4 = np.histogram(IPR_new4, bins=bins, normed=True)\n",
    "\n",
    "            \n",
    "        ax.plot((bin_edges2[1:]+bin_edges2[:-1])/2, hist2, 'o-',  color=color_list[1], label = r'$i=1$') \n",
    "        ax.fill_between((bin_edges2[1:]+bin_edges2[:-1])/2, hist2, 0, color=color_list[1], alpha=0.6)\n",
    "        \n",
    "        ax.plot((bin_edges1[1:]+bin_edges1[:-1])/2, hist1, 'o-',  color=color_list[0], label = r'$i=2$') \n",
    "        ax.fill_between((bin_edges1[1:]+bin_edges1[:-1])/2, hist1, 0, color=color_list[0], alpha=0.6)\n",
    "\n",
    "        ax.plot((bin_edges3[1:]+bin_edges3[:-1])/2, hist3, 'o-',  color=color_list[2], label = r'$i=3$') \n",
    "        ax.fill_between((bin_edges3[1:]+bin_edges3[:-1])/2, hist3, 0, color=color_list[2], alpha=0.6)\n",
    "        \n",
    "        ax.plot((bin_edges4[1:]+bin_edges4[:-1])/2, hist4, 'o-',  color=color_list[3], label = r'$i=4$') \n",
    "        ax.fill_between((bin_edges4[1:]+bin_edges4[:-1])/2, hist4, 0, color=color_list[3], alpha=0.6)\n",
    "\n",
    "        ax.legend(fontsize=fs-15)  \n",
    "        \n",
    "    ax.text(-0.11, 0.97, '(b)' ,transform= ax.transAxes, size=40,family='STIXGeneral')\n",
    "    \n",
    "plt.tight_layout()\n",
    "plt.savefig(path_figures + 'hist_D2.pdf',bbox_inches='tight')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# FIGURE 10 - SCALING"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "iterations = np.array([15,16,17,18,19])\n",
    "mu = 2\n",
    "alpha = 5\n",
    "delta = 0.8\n",
    "L = 1\n",
    "\n",
    "Fn_list = []\n",
    "\n",
    "IPR_mean1 = IPR_mean2 = IPR_mean3 = IPR_mean4 = []\n",
    "fig, ax = plt.subplots(nrows=1, ncols=1, sharex=False, sharey=False, figsize=(10, 7,))\n",
    "\n",
    "color_list = ['lightcoral','dodgerblue','seagreen','goldenrod']\n",
    "markers = ['o', 'd', 's', '*']\n",
    "for it in iterations:\n",
    "    \n",
    "    name = 'LR_alpha_%.2f_delta_%.2f' %(alpha, delta)\n",
    "\n",
    "    Fn1, Fn = Fibonacci(it)\n",
    "    Fn_list = np.append(Fn_list, Fn)\n",
    "    length = 1\n",
    "\n",
    "    IPR = np.load(path_data + 'IPR_ME_%s_it_%.0f_mu_%.0f.npy'%(name, it, mu))\n",
    "    evals = np.load(path_data + 'evals_ME_%s_it_%.0f_mu_%.0f.npy'%(name, it, mu))\n",
    "\n",
    "    IPR = IPR[evals>0]\n",
    "    evals = evals[evals>0]\n",
    "    \n",
    "    IPR_new = IPR    \n",
    "    \n",
    "    IPR_new1 = IPR_new[Fn1-int(0.09*Fn):Fn1]\n",
    "    IPR_mean1 = np.append(IPR_mean1, np.mean(abs(np.log(IPR_new1)/np.log(Fn))))\n",
    "    \n",
    "    IPR_new2 = IPR_new[0:Fn1-int(0.09*Fn)]\n",
    "    IPR_mean2 = np.append(IPR_mean2, np.mean(abs(np.log(IPR_new2)/np.log(Fn))))\n",
    "    \n",
    "    IPR_new3 = IPR_new[Fn1:Fn1+int(0.145*Fn)]\n",
    "    IPR_mean3 = np.append(IPR_mean3, np.mean(abs(np.log(IPR_new3)/np.log(Fn))))\n",
    "    \n",
    "    IPR_new4 = IPR_new[Fn1+int(0.145*Fn):]\n",
    "    IPR_mean4 = np.append(IPR_mean4, np.mean(abs(np.log(IPR_new4)/np.log(Fn))))\n",
    "\n",
    "    if it == 21:\n",
    "        ax = axes[0]\n",
    "        ax.plot(np.arange(Fn)[Fn1-int(0.09*Fn):Fn1]/Fn, abs(np.log(IPR_new1)/np.log(Fn)), '.-', color=color_list[0], linewidth=2)\n",
    "        ax.plot(np.arange(Fn)[0:Fn1-int(0.09*Fn)]/Fn, abs(np.log(IPR_new2)/np.log(Fn)), '.-', color=color_list[1], linewidth=2)\n",
    "        ax.plot(np.arange(Fn)[Fn1:Fn1+int(0.145*Fn)]/Fn, abs(np.log(IPR_new3)/np.log(Fn)), '.-', color=color_list[2], linewidth=2)\n",
    "        ax.plot(np.arange(Fn)[Fn1+int(0.145*Fn):]/Fn, abs(np.log(IPR_new4)/np.log(Fn)), '.-', color=color_list[3], linewidth=2)\n",
    "        ax.axvline(Fn1/Fn, color='k', linestyle='--', linewidth=3, alpha=1)\n",
    "        ax.axvline((Fn1-int(0.09*Fn))/Fn, color='k', linestyle='--', linewidth=3, alpha=1)    \n",
    "        ax.axvline((Fn1+int(0.145*Fn))/Fn, color='k', linestyle='--', linewidth=3, alpha=1)   \n",
    "        ax.set_xlim((Fn1-int(0.35*Fn))/Fn, (Fn-int(0.05*Fn))/Fn)\n",
    "        ax.set_ylim(0,1)\n",
    "        ax.set_xlabel(r'$n/N$', fontsize=fs)\n",
    "        ax.set_ylabel(r'$D_2$', fontsize=fs)\n",
    "        \n",
    "        ax.text(0.1, 0.2, r'$1$',\n",
    "            verticalalignment='bottom', horizontalalignment='right',\n",
    "            bbox={'facecolor': 'white', 'alpha': 0.7, 'pad':5},\n",
    "            color = 'k', transform=ax.transAxes, fontsize=fs)\n",
    "        ax.text(0.46, 0.3, r'$2$',\n",
    "            verticalalignment='bottom', horizontalalignment='right',\n",
    "            bbox={'facecolor': 'white', 'alpha': 0.7, 'pad': 5},\n",
    "            color = 'k', transform=ax.transAxes, fontsize=fs)\n",
    "        ax.text(0.6, 0.7, r'$3$',\n",
    "            verticalalignment='bottom', horizontalalignment='right',\n",
    "            bbox={'facecolor': 'white', 'alpha': 0.7, 'pad': 5},\n",
    "            color = 'k', transform=ax.transAxes, fontsize=fs)\n",
    "        ax.text(0.9, 0.5, r'$4$',\n",
    "            verticalalignment='bottom', horizontalalignment='right',\n",
    "            bbox={'facecolor': 'white', 'alpha': 0.7, 'pad': 5},\n",
    "            color = 'k', transform=ax.transAxes, fontsize=fs)\n",
    "        \n",
    "coef = np.polyfit(1/np.array(Fn_list), IPR_mean2, deg=2)\n",
    "x = np.linspace(0,1/Fn_list[0])\n",
    "ax.plot(x, coef[0]*x**2 + coef[1]*x + coef[2], '--', color='black', linewidth=1, alpha=1)\n",
    "ax.plot(1/Fn_list, IPR_mean2, markers[1], color=color_list[1], markersize=10, linewidth=2, alpha=0.9, label = r'$i=1$')\n",
    "\n",
    "coef = np.polyfit(1/np.array(Fn_list), IPR_mean1, deg=2)\n",
    "x = np.linspace(0,1/Fn_list[0])\n",
    "ax.plot(x, coef[0]*x**2 + coef[1]*x + coef[2], '--', color='black', linewidth=1, alpha=1)\n",
    "ax.plot(1/Fn_list, IPR_mean1, markers[0], color=color_list[0], markersize=10, linewidth=2, alpha=0.9, label = r'$i=2$') \n",
    "\n",
    "coef = np.polyfit(1/np.array(Fn_list), IPR_mean3, deg=2)\n",
    "x = np.linspace(0,1/Fn_list[0])\n",
    "ax.plot(x, coef[0]*x**2 + coef[1]*x + coef[2], '--', color='black', linewidth=1, alpha=1)\n",
    "ax.plot(1/Fn_list, IPR_mean3, markers[2], color=color_list[2], markersize=10, linewidth=2, alpha=0.9, label = r'$i=3$')\n",
    "\n",
    "coef = np.polyfit(1/np.array(Fn_list), IPR_mean4, deg=2)\n",
    "x = np.linspace(0,1/Fn_list[0])\n",
    "ax.plot(x, coef[0]*x**2 + coef[1]*x + coef[2], '--', color='black', linewidth=1, alpha=1)\n",
    "ax.plot(1/Fn_list, IPR_mean4, markers[3], color=color_list[3], markersize=10, linewidth=2, alpha=0.9, label = r'$i=4$')\n",
    "\n",
    "ax.set_xlim(0, 1/Fn_list[0])\n",
    "ax.set_ylim(-0.02,1)\n",
    "ax.set_xlabel(r'$1/N$', fontsize=fs)\n",
    "ax.set_ylabel(r'$\\bar{D}_2^i$', fontsize=fs)\n",
    "ax.legend(fontsize=fs-20, loc='lower right')  \n",
    "\n",
    "plt.tight_layout()\n",
    "plt.savefig(path_figures + 'scaling.pdf',bbox_inches='tight')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
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