otoc_exp.ipynb

{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "ename": "LoadError",
     "evalue": "LoadError: UndefVarError: inculde not defined\nin expression starting at /mnt/c/Users/xin/OneDrive/MBL/mbl/MBLpack.jl:6",
     "output_type": "error",
     "traceback": [
      "LoadError: UndefVarError: inculde not defined\nin expression starting at /mnt/c/Users/xin/OneDrive/MBL/mbl/MBLpack.jl:6",
      "",
      "Stacktrace:",
      " [1] top-level scope",
      "   @ /mnt/c/Users/xin/OneDrive/MBL/mbl/MBLpack.jl:6",
      " [2] include(fname::String)",
      "   @ Base.MainInclude ./client.jl:476",
      " [3] top-level scope",
      "   @ In[7]:1"
     ]
    }
   ],
   "source": [
    "include(\"MBLpack.jl\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [],
   "source": [
    "using Plots"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [],
   "source": [
    "nbit = 5;\n",
    "W = 5;\n",
    "j = 1;"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [],
   "source": [
    "zhai1 = xxz(nbit,1,0,5); #AL\n",
    "zhai2 = xxz(nbit,1,0.2,5); #MBL\n",
    "zhai3 = xxz(nbit,1,1,0); #thermal"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "ename": "LoadError",
     "evalue": "LoadError: ArgumentError: @threads requires a `for` loop expression\nin expression starting at In[5]:2",
     "output_type": "error",
     "traceback": [
      "LoadError: ArgumentError: @threads requires a `for` loop expression\nin expression starting at In[5]:2",
      "",
      "Stacktrace:",
      " [1] var\"@threads\"(__source__::LineNumberNode, __module__::Module, args::Vararg{Any})",
      "   @ Base.Threads ./threadingconstructs.jl:226"
     ]
    }
   ],
   "source": [
    "tlist = 10 .^ range(0,6,length=10);\n",
    "y1 = real([sum([inf_otoc(X,X; t=t,hamiltonian=zhai1,nbit=nbit, i=5,j=1) for _ in 1:10000])/10000 for t in tlist]);\n",
    "\n",
    "y2 = real([sum([inf_otoc(X,X; t=t,hamiltonian=zhai2,nbit=nbit, i=5,j=1) for _ in 1:10000])/10000 for t in tlist]);\n",
    "y3 = real([inf_otoc(X,X; t=t,hamiltonian=zhai3,nbit=nbit, i=5,j=1)  for t in tlist]);"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {},
   "outputs": [
    {
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     },
     "execution_count": 17,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "\n",
    "Plots.scatter(tlist,[y1,y2,y3],ms=2,label=[\"AL\" \"MBL\" \"Thermal\"],legend=:outertopright,xscale=:log10)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {},
   "outputs": [
    {
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      ]
     },
     "execution_count": 18,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "tlist = range(0,6,length=60);\n",
    "y1 = real([sum([inf_otoc(X,X; t=t,hamiltonian=zhai1,nbit=nbit, i=5,j=1) for _ in 1:10000])/10000 for t in tlist]);\n",
    "y2 = real([sum([inf_otoc(X,X; t=t,hamiltonian=zhai2,nbit=nbit, i=5,j=1) for _ in 1:10000])/10000 for t in tlist]);\n",
    "y3 = real([inf_otoc(X,X; t=t,hamiltonian=zhai3,nbit=nbit, i=5,j=1)  for t in tlist]);\n",
    "Plots.scatter(tlist,[y1,y2,y3],ms=2,label=[\"AL\" \"MBL\" \"Thermal\"],legend=:outertopright)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {},
   "outputs": [
    {
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      ]
     },
     "execution_count": 19,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "tlist = range(0,6,length=60);\n",
    "y1 = real([sum([inf_otoc(X,Y; t=t,hamiltonian=zhai1,nbit=nbit, i=5,j=1) for _ in 1:10000])/10000 for t in tlist]);\n",
    "y2 = real([sum([inf_otoc(X,Y; t=t,hamiltonian=zhai2,nbit=nbit, i=5,j=1) for _ in 1:10000])/10000 for t in tlist]);\n",
    "y3 = real([inf_otoc(X,Y; t=t,hamiltonian=zhai3,nbit=nbit, i=5,j=1)  for t in tlist]);\n",
    "Plots.scatter(tlist,[y1,y2,y3],ms=2,label=[\"AL\" \"MBL\" \"Thermal\"],legend=:outertopright)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {},
   "outputs": [
    {
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      ]
     },
     "execution_count": 18,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "tlist = range(0,6,length=60);\n",
    "y1 = real([sum([inf_otoc(X,Z; t=t,hamiltonian=zhai1,nbit=nbit, i=5,j=1) for _ in 1:10000])/10000 for t in tlist]);\n",
    "y2 = real([sum([inf_otoc(X,Z; t=t,hamiltonian=zhai2,nbit=nbit, i=5,j=1) for _ in 1:10000])/10000 for t in tlist]);\n",
    "y3 = real([inf_otoc(X,X; t=t,hamiltonian=zhai3,nbit=nbit, i=5,j=1)  for t in tlist]);\n",
    "Plots.scatter(tlist,[y1,y2,y3],ms=2,label=[\"AL\" \"MBL\" \"Thermal\"],legend=:outertopright)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {},
   "outputs": [
    {
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      ]
     },
     "execution_count": 16,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "tlist = 10 .^ range(-4,10,length = 60);\n",
    "y1 = real([sum([inf_otoc(X,X; t=t,hamiltonian=zhai1,nbit=nbit, i=5,j=1) for _ in 1:1000])/1000 for t in tlist]);\n",
    "y2 = real([sum([inf_otoc(X,X; t=t,hamiltonian=zhai2,nbit=nbit, i=5,j=1) for _ in 1:1000])/1000 for t in tlist]);\n",
    "y3 = real([sum([inf_otoc(X,X; t=t,hamiltonian=zhai3,nbit=nbit, i=5,j=1) for _ in 1:1000])/1000 for t in tlist]);\n",
    "Plots.scatter(tlist,[y1,y2,y3],ms=2,label=[\"AL\" \"MBL\" \"Thermal\"],legend=:outertopright,xscale=:log10)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {},
   "outputs": [
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     },
     "execution_count": 19,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "tlist = 10 .^ range(-4,10,length = 60);\n",
    "y1 = real([sum([inf_otoc(X,Y; t=t,hamiltonian=zhai1,nbit=nbit, i=5,j=1) for _ in 1:1000])/1000 for t in tlist]);\n",
    "y2 = real([sum([inf_otoc(X,Y; t=t,hamiltonian=zhai2,nbit=nbit, i=5,j=1) for _ in 1:1000])/1000 for t in tlist]);\n",
    "y3 = real([sum([inf_otoc(X,Y; t=t,hamiltonian=zhai3,nbit=nbit, i=5,j=1) for _ in 1:1000])/1000 for t in tlist]);\n",
    "Plots.scatter(tlist,[y1,y2,y3],ms=2,label=[\"AL\" \"MBL\" \"Thermal\"],legend=:outertopright,xscale=:log10)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {},
   "outputs": [
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      ]
     },
     "execution_count": 21,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "tlist = 10 .^ range(-4,10,length = 60);\n",
    "y1 = real([sum([inf_otoc(Z,Z; t=t,hamiltonian=zhai1,nbit=nbit, i=5,j=1) for _ in 1:1000])/1000 for t in tlist]);\n",
    "y2 = real([sum([inf_otoc(Z,Z; t=t,hamiltonian=zhai2,nbit=nbit, i=5,j=1) for _ in 1:1000])/1000 for t in tlist]);\n",
    "y3 = real([sum([inf_otoc(Z,Z; t=t,hamiltonian=zhai3,nbit=nbit, i=5,j=1) for _ in 1:1000])/1000 for t in tlist]);\n",
    "Plots.scatter(tlist,[y1,y2,y3],ms=2,label=[\"AL\" \"MBL\" \"Thermal\"],legend=:outertopright,xscale=:log10)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {},
   "outputs": [
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      ]
     },
     "execution_count": 20,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "tlist = 10 .^ range(-4,10,length = 60);\n",
    "y1 = real([sum([inf_otoc(X,Z; t=t,hamiltonian=zhai1,nbit=nbit, i=5,j=1) for _ in 1:1000])/1000 for t in tlist]);\n",
    "y2 = real([sum([inf_otoc(X,Z; t=t,hamiltonian=zhai2,nbit=nbit, i=5,j=1) for _ in 1:1000])/1000 for t in tlist]);\n",
    "y3 = real([sum([inf_otoc(X,Z; t=t,hamiltonian=zhai3,nbit=nbit, i=5,j=1) for _ in 1:1000])/1000 for t in tlist]);\n",
    "Plots.scatter(tlist,[y1,y2,y3],ms=2,label=[\"AL\" \"MBL\" \"Thermal\"],legend=:outertopright,xscale=:log10)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 8 - Sites \n",
    "### Interval is 5, according to SinceBullenti,"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "metadata": {},
   "outputs": [],
   "source": [
    "## 6nbits"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "metadata": {},
   "outputs": [
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2024.35,1123.18 2026.39,1122.16 2028.43,1121.19 2030.47,1120.27 2032.51,1119.39 2034.55,1118.57 2036.59,1117.81 2038.63,1117.11 2040.67,1116.47 2042.71,1115.9 2044.75,1115.4 2046.79,1114.97 2048.83,1114.61 2050.87,1114.32 2052.91,1114.12 2054.95,1113.99 2056.99,1113.95 2059.03,1113.98 2061.07,1114.1 2063.11,1114.3 2065.15,1114.58 2067.19,1114.95 2069.23,1115.41 2071.27,1115.94 2073.31,1116.57 2075.35,1117.27 2077.39,1118.07 2079.43,1118.94 2081.47,1119.9 2083.51,1120.93 2085.55,1122.05 2087.6,1123.24 2089.64,1124.52 2091.68,1125.86 2093.72,1127.28 2095.76,1128.77 2097.8,1130.33 2099.84,1131.95 2101.88,1133.64 2103.92,1135.39 2105.96,1137.2 2108,1139.06 2110.04,1140.97 2112.08,1142.94 2114.12,1144.95 2116.16,1147 2118.2,1149.09 2120.24,1151.22 2122.28,1153.38 2124.32,1155.57 2126.36,1157.78 2128.4,1160.02 2130.44,1162.27 2132.48,1164.54 2134.52,1166.82 2136.56,1169.11 2138.6,1171.4 2140.64,1173.69 2142.68,1175.98 2144.72,1178.26 2146.76,1180.53 2148.8,1182.79 2150.84,1185.03 2152.88,1187.25 2154.92,1189.44 2156.96,1191.61 2159,1193.75 2161.04,1195.85 2163.08,1197.92 2165.12,1199.95 2167.16,1201.94 2169.2,1203.88 2171.24,1205.77 2173.28,1207.62 2175.32,1209.42 2177.36,1211.16 2179.4,1212.84 2181.44,1214.47 2183.48,1216.04 2185.52,1217.55 2187.56,1219 2189.6,1220.38 2191.64,1221.69 2193.68,1222.94 2195.72,1224.13 2197.76,1225.24 2199.8,1226.29 2201.84,1227.27 2203.88,1228.18 2205.92,1229.02 2207.97,1229.79 2210.01,1230.49 2212.05,1231.12 2214.09,1231.69 2216.13,1232.18 2218.17,1232.61 2220.21,1232.97 2222.25,1233.27 2224.29,1233.5 2226.33,1233.67 2228.37,1233.77 2230.41,1233.82 2232.45,1233.8 2234.49,1233.73 2236.53,1233.6 2238.57,1233.42 2240.61,1233.18 2242.65,1232.89 2244.69,1232.56 2246.73,1232.18 2248.77,1231.75 2250.81,1231.29 2252.85,1230.78 2254.89,1230.24 2256.93,1229.67 2258.97,1229.06 2261.01,1228.42 2263.05,1227.76 2265.09,1227.08 2267.13,1226.37 2269.17,1225.64 2271.21,1224.9 2273.25,1224.15 2275.29,1223.39 2277.33,1222.62 2279.37,1221.84 2281.41,1221.06 2283.45,1220.29 2285.49,1219.52 2287.53,1218.75 2289.57,1217.99 2291.61,1217.25 \"/>\n",
       "<path clip-path=\"url(#clip030)\" d=\"M2012.27 198.898 L2280.74 198.898 L2280.74 95.2176 L2012.27 95.2176  Z\" fill=\"#ffffff\" fill-rule=\"evenodd\" fill-opacity=\"1\"/>\n",
       "<polyline clip-path=\"url(#clip030)\" style=\"stroke:#000000; stroke-linecap:round; stroke-linejoin:round; stroke-width:4; stroke-opacity:1; fill:none\" points=\"2012.27,198.898 2280.74,198.898 2280.74,95.2176 2012.27,95.2176 2012.27,198.898 \"/>\n",
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       "<path clip-path=\"url(#clip030)\" d=\"M2218.15 166.745 Q2216.34 171.375 2214.63 172.787 Q2212.92 174.199 2210.05 174.199 L2206.65 174.199 L2206.65 170.634 L2209.15 170.634 Q2210.9 170.634 2211.88 169.8 Q2212.85 168.967 2214.03 165.865 L2214.79 163.921 L2204.31 138.412 L2208.82 138.412 L2216.92 158.689 L2225.02 138.412 L2229.54 138.412 L2218.15 166.745 Z\" fill=\"#000000\" fill-rule=\"evenodd\" fill-opacity=\"1\" /><path clip-path=\"url(#clip030)\" d=\"M2236.83 160.402 L2244.47 160.402 L2244.47 134.037 L2236.16 135.703 L2236.16 131.444 L2244.42 129.778 L2249.1 129.778 L2249.1 160.402 L2256.74 160.402 L2256.74 164.338 L2236.83 164.338 L2236.83 160.402 Z\" fill=\"#000000\" fill-rule=\"evenodd\" fill-opacity=\"1\" /></svg>\n"
      ]
     },
     "execution_count": 26,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "nmr1 = nmr_ising(4,1,0);\n",
    "nmr2 = nmr_ising(4,1.05,0.5);\n",
    "tlist = range(0,7,1000);\n",
    "otoc1 = real([inf_otoc(X, Y;t=t,hamiltonian=nmr2,nbit=4,i=1,j=4) for t in tlist]);\n",
    "plot(tlist,otoc1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "function heisenberg(nbit::Int;periodic::Bool=false)\n",
    "    sx = i ->  1/2 * put(nbit, i=>X)\n",
    "    sy = i ->  1/2 * put(nbit, i=>Y)\n",
    "    sz = i ->  1/2 * put(nbit, i=>Z)\n",
    "    hopping = map(1:nbit) do i\n",
    "\t\tj = i%(nbit-1) + 1\n",
    "\t\t(sx(i)*sx(j)+sy(i)*sy(j)+sz(i)*sz(j))\n",
    "\tend |> sum\n",
    "    return hopping\n",
    "end\n",
    "hprime = heisenberg(8)\n",
    "yprime = real([inf_otoc(X,X;t=t, hamiltonian=h, nbit=nbit,i=8,j=1) for t Base.RangeVecIntList])\n",
    "plot(tlist,yprime)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "hei0 = hamiltonian(nbit,0)\n",
    "hei1 = hamiltonian(nbit,5); #ETH\n",
    "hei2 = hamiltonian(nbit,40); #MBL\n",
    "# W = 0\n",
    "otoc0 = real([inf_otoc(X, X;t=t,hamiltonian=hei0,nbit=nbit,i=1,j=8) for t in tlist]);\n",
    "# ETH OTOC\n",
    "otoc1 = real([inf_otoc(X, X;t=t,hamiltonian=hei1,nbit=nbit,i=1,j=8) for t in tlist]);\n",
    "# MBL OTOC\n",
    "otoc2 = real([inf_otoc(X, X;t=t,hamiltonian=hei2,nbit=nbit,i=1,j=8) for t in tlist]);"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "scatter(tlist,[otoc0, otoc1, otoc2],ms=2,label=[\"W=0\" \"ETH\" \"MBL\"])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "log10.(1:1e5)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "zhai1 = xxz(nbit,10,0,50); #AL\n",
    "zhai2 = xxz(nbit,10,2,50); #MBL\n",
    "zhai3 = xxz(nbit,10,2,0); #thermal"
   ]
  }
 ],
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