spin_chain.ipynb

{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "import matplotlib as plt\n",
    "from qutip import *\n",
    "import time"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "$H =  - \\sum\\limits_{j = 1}^N {\\vec h{{\\vec \\sigma }_j} - J} \\sum\\limits_{j = 1}^{N - 1} {{{\\vec \\sigma }_j}{{\\vec \\sigma }_{j + 1}}}$\n",
    "\n",
    "${h_x}(t) = \\sin (\\frac{{{v^2}{t^2}}}{{2\\pi }})$\n",
    "\n",
    "${h_z}(t) = \\cos (\\frac{{{v^2}{t^2}}}{{2\\pi }})$\n",
    "\n",
    "${h_y}(t) = 0$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "def ExpectofSpinChain(N,J,hx,hy,hz,time_list):\n",
    "    #psi0 is the initial state\n",
    "    #N(int) is the number of spins\n",
    "    #J(int) is the interacting strength\n",
    "    #{hx,hy,hz}(string) is the strength of the magnetic field and input as string type.\n",
    "    #time_list(list[]) define the time list for solving SE equantion\n",
    "    si = qeye(2)\n",
    "    sx = sigmax()\n",
    "    sy = sigmay()\n",
    "    sz = sigmaz()\n",
    "    #define some abbr\n",
    "    sx_list = []\n",
    "    sy_list = []\n",
    "    sz_list = []\n",
    "    for n in range(N):\n",
    "        op_list = []\n",
    "        for m in range(N):\n",
    "            op_list.append(si)\n",
    "\n",
    "        op_list[n] = sx\n",
    "        sx_list.append(tensor(op_list))\n",
    "\n",
    "        op_list[n] = sy\n",
    "        sy_list.append(tensor(op_list))\n",
    "\n",
    "        op_list[n] = sz\n",
    "        sz_list.append(tensor(op_list))\n",
    "    #construct a Operator List for convenience.\n",
    "    H0 = 0\n",
    "    for n in range(N-1):\n",
    "        H0 += -  J * sx_list[n] * sx_list[n+1]\n",
    "        H0 += -  J * sy_list[n] * sy_list[n+1]\n",
    "        H0 += -  J * sz_list[n] * sz_list[n+1]\n",
    "    #construct the static part of Hamiltonian\n",
    "    H_dynamic_x = 0\n",
    "    for n in range(N):\n",
    "        H_dynamic_x += -  sx_list[n]\n",
    "    H_dynamic_y = 0\n",
    "    for n in range(N):\n",
    "        H_dynamic_y += -  sy_list[n]\n",
    "    H_dynamic_z = 0\n",
    "    for n in range(N):\n",
    "        H_dynamic_z += -  sz_list[n]\n",
    "    #construct the dynamical parts of Hamitonian\n",
    "    psi0 = (H0 + H_dynamic_z).groundstate()[1]\n",
    "    #construct the initial state\n",
    "    H = [H0,[H_dynamic_x,hx],[H_dynamic_y,hy],[H_dynamic_z,hz]]\n",
    "    result = mesolve(H,psi0,time_list,[],sy_list)\n",
    "    return result.expect"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "6179.41600013\n"
     ]
    }
   ],
   "source": [
    "start_time = time.time()\n",
    "def hx(t,args):\n",
    "    return np.sin(0.01*t*t/(2*np.pi))\n",
    "def hz(t,args):\n",
    "    return np.cos(0.01*t*t/(2*np.pi))\n",
    "def hy(t,args):\n",
    "    return 0\n",
    "# the configuration of magnetic field,fixed v = 0.1\n",
    "N = 10\n",
    "step_of_J = 100\n",
    "J =  np.linspace(-1.6,0.1,step_of_J)\n",
    "step = 100\n",
    "# the step of time list\n",
    "t_list = np.linspace(0,np.pi/0.1,step)\n",
    "my = []\n",
    "for i in range(step_of_J):\n",
    "    temp = 0\n",
    "    for n in range(N):\n",
    "        temp += ExpectofSpinChain(N,J[i],hx,hy,hz,t_list)[n][step-1]/0.1 \n",
    "    my.append(temp)\n",
    "end_time = time.time()\n",
    "print end_time - start_time"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "3192.71399999\n"
     ]
    }
   ],
   "source": [
    "start_time = time.time()\n",
    "def hx(t,args):\n",
    "    return np.sin(0.01*t*t/(2*np.pi))\n",
    "def hz(t,args):\n",
    "    return np.cos(0.01*t*t/(2*np.pi))\n",
    "def hy(t,args):\n",
    "    return 0\n",
    "# the configuration of magnetic field,fixed v = 0.1\n",
    "# In Windows, strings can cause an issue.I guess it's cython that not work well on my machine\n",
    "N_1 = 9\n",
    "step_of_J = 100\n",
    "J =  np.linspace(-1.6,0.1,step_of_J)\n",
    "step = 100\n",
    "# the step of time list\n",
    "t_list = np.linspace(0,np.pi/0.1,step)\n",
    "my_1 = []\n",
    "for i in range(step_of_J):\n",
    "    temp = 0\n",
    "    for n in range(N_1):\n",
    "        temp += ExpectofSpinChain(N_1,J[i],hx,hy,hz,t_list)[n][step-1]/0.1 \n",
    "    my_1.append(temp)\n",
    "end_time = time.time()\n",
    "print end_time - start_time"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "fig , ax = plt.pyplot.subplots()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.legend.Legend at 0xe4232e8>"
      ]
     },
     "execution_count": 11,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "ax.clear()\n",
    "ax.plot(J,my,'ro-')\n",
    "ax.plot(J,my_1,'o--')\n",
    "ax.set_xlabel('J(Strength of Interacition)')\n",
    "ax.set_ylabel('${F_{\\phi \\theta }}$')\n",
    "ax.set_title('The Berry Curvature in Heisenberg Spin Chain')\n",
    "ax.legend(('$N=10$','$N=9$'))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
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99x79/ZJLLnHHHnts1vu77LLL3Pz5811FRYVraGhwd95559G2Bx54wJ1wwgnuNa95jfvs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\nkiSpYwZakiRJktQxAy1JkiRJ6tj/A0j2pcTU2cKaAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0xd6c88d0>"
      ]
     },
     "execution_count": 12,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "fig.set_size_inches(14.5, 8)\n",
    "fig"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "<table><tr><th>Software</th><th>Version</th></tr><tr><td>QuTiP</td><td>4.0.2</td></tr><tr><td>Numpy</td><td>1.12.0</td></tr><tr><td>SciPy</td><td>0.18.1</td></tr><tr><td>matplotlib</td><td>2.0.0</td></tr><tr><td>Cython</td><td>0.25.2</td></tr><tr><td>Number of CPUs</td><td>2</td></tr><tr><td>BLAS Info</td><td>OPENBLAS</td></tr><tr><td>IPython</td><td>5.1.0</td></tr><tr><td>Python</td><td>2.7.13 |Anaconda 4.3.0 (x86_64)| (default, Dec 20 2016, 23:05:08) \n",
       "[GCC 4.2.1 Compatible Apple LLVM 6.0 (clang-600.0.57)]</td></tr><tr><td>OS</td><td>posix [darwin]</td></tr><tr><td colspan='2'>Mon Mar 06 10:58:36 2017 CST</td></tr></table>"
      ],
      "text/plain": [
       "<IPython.core.display.HTML object>"
      ]
     },
     "execution_count": 4,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "from qutip.ipynbtools import version_table\n",
    "\n",
    "version_table()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "collapsed": true
   },
   "source": [
    "$$H = {a^ + }a$$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": []
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 2",
   "language": "python",
   "name": "python2"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 2
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython2",
   "version": "2.7.13"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 2
}