examples/heom/heom-5a-fermions-single-impurity-model.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Example 5a: Fermionic single impurity model\n",
    "\n",
    "## Example of the Fermionic HEOM solver\n",
    "\n",
    "Here we model a single fermion coupled to two electronic leads or reservoirs (e.g.,  this can describe a single quantum dot, a molecular transistor, etc).  Note that in this implementation we primarily follow the definitions used by Christian Schinabeck in his Dissertation https://opus4.kobv.de/opus4-fau/files/10984/DissertationChristianSchinabeck.pdf and related publications.\n",
    "\n",
    "\n",
    "Notation:  \n",
    "$K=L/R$ refers to  left or right leads.\n",
    "\n",
    "$\\sigma=\\pm$ refers to input/output\n",
    "\n",
    "\n",
    "We choose a Lorentzian spectral density for the leads, with a peak at the chemical potential. The latter simplifies a little the notation required for the correlation functions, but can be relaxed if neccessary.\n",
    "\n",
    "$$J(\\omega) = \\frac{\\Gamma  W^2}{((\\omega-\\mu_K)^2 +W^2 )}$$\n",
    "\n",
    "\n",
    "Fermi distribution is\n",
    "\n",
    "$$f_F (x) = (\\exp(x) + 1)^{-1}$$\n",
    "\n",
    "gives correlation functions\n",
    "\n",
    "$$C^{\\sigma}_K(t) = \\frac{1}{2\\pi} \\int_{-\\infty}^{\\infty} d\\omega e^{\\sigma i \\omega t} \\Gamma_K(\\omega) f_F[\\sigma\\beta(\\omega - \\mu)]$$\n",
    "\n",
    "\n",
    "As with the Bosonic case we can treat these with Matsubara, Pade, or fitting approaches.\n",
    "\n",
    "The Pade decomposition approximates the Fermi distubition as \n",
    "\n",
    "$$f_F(x) \\approx f_F^{\\mathrm{approx}}(x) = \\frac{1}{2} - \\sum_l^{l_{max}} \\frac{2k_l x}{x^2 + \\epsilon_l^2}$$\n",
    "\n",
    "$k_l$ and $\\epsilon_l$ are co-efficients defined in J. Chem Phys 133,10106\n",
    "\n",
    "Evaluating the integral for the correlation functions gives,\n",
    "\n",
    "\n",
    "$$C_K^{\\sigma}(t) \\approx \\sum_{l=0}^{l_{max}} \\eta_K^{\\sigma_l} e^{-\\gamma_{K,\\sigma,l}t}$$\n",
    "\n",
    "where\n",
    "\n",
    "$$\\eta_{K,0} = \\frac{\\Gamma_KW_K}{2} f_F^{approx}(i\\beta_K W)$$\n",
    "\n",
    "$$\\gamma_{K,\\sigma,0} = W_K - \\sigma i\\mu_K$$ \n",
    "\n",
    "$$\\eta_{K,l\\neq 0} = -i\\cdot \\frac{k_m}{\\beta_K} \\cdot \\frac{\\Gamma_K W_K^2}{-\\frac{\\epsilon^2_m}{\\beta_K^2} + W_K^2}$$\n",
    "\n",
    "$$\\gamma_{K,\\sigma,l\\neq 0}= \\frac{\\epsilon_m}{\\beta_K} - \\sigma i \\mu_K$$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Populating the interactive namespace from numpy and matplotlib\n"
     ]
    }
   ],
   "source": [
    "%load_ext autoreload\n",
    "%autoreload 2\n",
    "%pylab inline"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "from qutip import *"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "metadata": {},
   "outputs": [],
   "source": [
    "import contextlib\n",
    "import time\n",
    "\n",
    "import numpy as np\n",
    "\n",
    "from qutip import *\n",
    "from qutip.nonmarkov.heom import HEOMSolver\n",
    "from qutip.nonmarkov.heom import FermionicBath\n",
    "from qutip.nonmarkov.heom import LorentzianBath\n",
    "from qutip.nonmarkov.heom import LorentzianPadeBath\n",
    "from scipy.integrate import quad"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [],
   "source": [
    "#Define parameters and plot lead spectra\n",
    "\n",
    "Gamma = 0.01  #coupling strength\n",
    "W=1. #cut-off\n",
    "T = 0.025851991 #temperature\n",
    "beta = 1./T\n",
    "\n",
    "theta = 2. #Bias\n",
    "mu_l = theta/2.\n",
    "mu_r = -theta/2.\n",
    "\n",
    "w_list = np.linspace(-2,2,100)\n",
    "\n",
    "def Gamma_L_w(w):\n",
    "    return Gamma*W**2/((w-mu_l)**2 + W**2)\n",
    "\n",
    "def Gamma_R_w(w):\n",
    "    return Gamma*W**2/((w-mu_r)**2 + W**2)\n",
    "\n",
    "\n",
    "def f(x):\n",
    "    kB=1.\n",
    "    return 1/(exp(x)+1.)\n",
    "def f2(x):\n",
    "    return 0.5"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.legend.Legend at 0x7f456a42a250>"
      ]
     },
     "execution_count": 4,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
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\n",
      "text/plain": [
       "<Figure size 864x504 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig, ax1 = plt.subplots(figsize=(12, 7))\n",
    "gam_list_in = [Gamma_L_w(w)*f(beta*(w-mu_l)) for w in w_list]\n",
    "\n",
    "ax1.plot(w_list,gam_list_in, \"b--\", linewidth=3, label= r\"S_L(w) input (absorption)\")\n",
    "\n",
    "\n",
    "ax1.set_xlabel(\"w\")\n",
    "ax1.set_ylabel(r\"$S(\\omega)$\")\n",
    "ax1.legend()\n",
    "\n",
    "\n",
    "gam_list_out = [Gamma_L_w(w)*f(-beta*(w-mu_l)) for w in w_list]\n",
    "spec = [Gamma_L_w(w) for w in w_list]\n",
    "\n",
    "ax1.plot(w_list,gam_list_out, \"r--\", linewidth=3, label= r\"S_L(w) output (emission)\")\n",
    "\n",
    "\n",
    "gam_list_in = [Gamma_R_w(w)*f(beta*(w-mu_r)) for w in w_list]\n",
    "\n",
    "ax1.plot(w_list,gam_list_in, \"b\", linewidth=3, label= r\"S_R(w) input (absorption)\")\n",
    "\n",
    "\n",
    "\n",
    "\n",
    "gam_list_out = [Gamma_R_w(w)*f(-beta*(w-mu_r)) for w in w_list]\n",
    "spec = [Gamma_R_w(w) for w in w_list]\n",
    "\n",
    "ax1.plot(w_list,gam_list_out, \"r\", linewidth=3, label= r\"S_R(w) output (emission)\")\n",
    "ax1.set_xlabel(\"w\")\n",
    "ax1.set_ylabel(r\"$n$\")\n",
    "ax1.legend()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 37,
   "metadata": {},
   "outputs": [],
   "source": [
    "#heom simulation with above params (Pade)\n",
    "options = Options(nsteps=15000, store_states=True, rtol=1e-14, atol=1e-14)\n",
    "\n",
    "#Single fermion.\n",
    "d1 = destroy(2)\n",
    "\n",
    "#Site energy\n",
    "e1 = 1. \n",
    "\n",
    "\n",
    "H0 = e1*d1.dag()*d1 \n",
    "\n",
    "Nk = 10\n",
    "Ncc = 2  #For a single impurity we converge with Ncc = 2\n",
    "\n",
    "Q=d1\n",
    "#bath = FermionicBath(Q, ck_plus, vk_plus, ck_minus, vk_minus)\n",
    "\n",
    "bathL = LorentzianPadeBath(Q,Gamma,W,mu_l,T,Nk,tag=\"L\")\n",
    "bathR = LorentzianPadeBath(Q,Gamma,W,mu_r,T,Nk,tag=\"R\")\n",
    "        # for a single impurity we converge with max_depth = 2\n",
    "resultHEOMP = HEOMSolver(H0, [bathL,bathR], 2, options=options)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 40,
   "metadata": {},
   "outputs": [],
   "source": [
    "rho_0 = basis(2,0)*basis(2,0).dag()\n",
    "\n",
    "\n",
    "rhossP,fullssP=resultHEOMP.steady_state()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 41,
   "metadata": {},
   "outputs": [],
   "source": [
    "rho_0 = basis(2,0)*basis(2,0).dag()\n",
    "tlist = np.linspace(0,100,1000)\n",
    "out1P = resultHEOMP.run(rho_0,tlist,ado_return=True)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "First we plot the decay of an initiall excited impurity. This is not very illuminating."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 42,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.legend.Legend at 0x7f4547207610>"
      ]
     },
     "execution_count": 42,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 576x576 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Plot the results\n",
    "fig, axes = plt.subplots(1, 1, sharex=True, figsize=(8,8))\n",
    "\n",
    "axes.plot(tlist, expect(out1P.states,rho_0), 'r--', linewidth=2, label=\"P11  \")\n",
    "axes.set_xlabel(r't', fontsize=28)\n",
    "axes.legend(loc=0, fontsize=12)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 43,
   "metadata": {},
   "outputs": [],
   "source": [
    "#heom simu on above params (Matsubara)\n",
    "\n",
    "\n",
    "#heom simulation with above params (Pade)\n",
    "options = Options(nsteps=15000, store_states=True, rtol=1e-14, atol=1e-14)\n",
    "\n",
    "#Single fermion.\n",
    "d1 = destroy(2)\n",
    "\n",
    "#Site energy\n",
    "e1 = 1. \n",
    "\n",
    "\n",
    "H0 = e1*d1.dag()*d1 \n",
    "\n",
    "Nk = 10\n",
    "Ncc = 2  #For a single impurity we converge with Ncc = 2\n",
    "\n",
    "Q=d1\n",
    "#bath = FermionicBath(Q, ck_plus, vk_plus, ck_minus, vk_minus)\n",
    "\n",
    "bathL = LorentzianBath(Q,Gamma,W,mu_l,T,Nk,tag=\"L\")\n",
    "bathR = LorentzianBath(Q,Gamma,W,mu_r,T,Nk,tag=\"R\")\n",
    "        # for a single impurity we converge with max_depth = 2\n",
    "resultHEOMM = HEOMSolver(H0, [bathL,bathR], Ncc, options=options)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 47,
   "metadata": {},
   "outputs": [],
   "source": [
    "out1M = resultHEOMM.run(rho_0,tlist,ado_return=True)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 45,
   "metadata": {},
   "outputs": [],
   "source": [
    "rhossHM,fullssM = resultHEOMM.steady_state()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We see a marked difference in the Matsubara vs Pade approach."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 48,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.legend.Legend at 0x7f45448de670>"
      ]
     },
     "execution_count": 48,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 576x576 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Plot the results\n",
    "fig, axes = plt.subplots(1, 1, sharex=True, figsize=(8,8))\n",
    "\n",
    "axes.plot(tlist, expect(out1P.states,rho_0), 'r--', linewidth=2, label=\"P11 Pade \")\n",
    "\n",
    "\n",
    "axes.plot(tlist, expect(out1M.states,rho_0), 'b--', linewidth=2, label=\"P12 Mats C\")\n",
    "\n",
    "axes.set_ylabel(r\"$\\rho_{11}$\")\n",
    "axes.set_xlabel(r't', fontsize=28)\n",
    "\n",
    "\n",
    "axes.legend(loc=0, fontsize=12)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "One advantage of this simple model is the current is analytically solvable, so we can check convergence of the result\n",
    "See the paper for a detailed description and references."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 60,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "(0.0008130726698759556+0j)\n"
     ]
    }
   ],
   "source": [
    "def Gamma_w(w, mu):\n",
    "    return Gamma*W**2/((w-mu)**2 + W**2)\n",
    "\n",
    "def CurrFunc():\n",
    "    def lamshift(w,mu):\n",
    "        return (w-mu)*Gamma_w(w,mu)/(2*W)\n",
    "    integrand = lambda w: ((2/(pi))*Gamma_w(w,mu_l)*Gamma_w(w,mu_r)*(f(beta*(w-mu_l))-f(beta*(w-mu_r))) /\n",
    "            ((Gamma_w(w,mu_l)+Gamma_w(w,mu_r))**2 +4*(w-e1 - lamshift(w,mu_l)-lamshift(w,mu_r))**2))\n",
    "    def real_func(x):\n",
    "        return real(integrand(x))\n",
    "    def imag_func(x):\n",
    "        return imag(integrand(x))\n",
    "\n",
    "    #in principle the bounds should be checked if parameters are changed\n",
    "    a= -2\n",
    "    b=2\n",
    "    real_integral = quad(real_func, a, b)\n",
    "    imag_integral = quad(imag_func, a, b)\n",
    "    \n",
    "   \n",
    "\n",
    "    return real_integral[0] + 1.0j * imag_integral[0]\n",
    "    \n",
    "curr_ana = CurrFunc()\n",
    "print(curr_ana)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 65,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "(0.0008130302805827144+5.421010862427522e-20j)\n",
      "(-1.0842021724855044e-19+1.6263032587282567e-19j)\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/tmp/ipykernel_5834/2194045410.py:13: DeprecationWarning: Calling np.sum(generator) is deprecated, and in the future will give a different result. Use np.sum(np.fromiter(generator)) or the python sum builtin instead.\n",
      "  return -1.0j * sum(\n"
     ]
    }
   ],
   "source": [
    "def state_current(ado_state,bath_tag):\n",
    "        level_1_aux = [\n",
    "            (ado_state.extract(label), ado_state.exps(label)[0])\n",
    "            for label in ado_state.filter(level=1,tags =[bath_tag])\n",
    "        ]\n",
    "        def exp_sign(exp):\n",
    "            return 1 if exp.type == exp.types[\"+\"] else -1\n",
    "\n",
    "        def exp_op(exp):\n",
    "            return exp.Q if exp.type == exp.types[\"+\"] else exp.Q.dag()\n",
    "\n",
    "        k = Nk + 1\n",
    "        return -1.0j * sum(\n",
    "            exp_sign(exp) * (exp_op(exp) * aux).tr()\n",
    "            for aux, exp in level_1_aux         \n",
    "        )\n",
    "        \n",
    "currP = state_current(fullssP,\"R\")\n",
    "print(currP)\n",
    "#The sum of the currents in the steadystate = 0\n",
    "print(state_current(fullssP,\"L\")+state_current(fullssP,\"R\"))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 62,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "(0.0011018485316349562-0j)\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/tmp/ipykernel_5834/349278954.py:13: DeprecationWarning: Calling np.sum(generator) is deprecated, and in the future will give a different result. Use np.sum(np.fromiter(generator)) or the python sum builtin instead.\n",
      "  return -1.0j * sum(\n"
     ]
    }
   ],
   "source": [
    "\n",
    "def state_current(ado_state,bath_tag):\n",
    "        level_1_aux = [\n",
    "            (ado_state.extract(label), ado_state.exps(label)[0])\n",
    "            for label in ado_state.filter(level=1,tags =[bath_tag])\n",
    "        ]\n",
    "        def exp_sign(exp):\n",
    "            return 1 if exp.type == exp.types[\"+\"] else -1\n",
    "\n",
    "        def exp_op(exp):\n",
    "            return exp.Q if exp.type == exp.types[\"+\"] else exp.Q.dag()\n",
    "\n",
    "        k = Nk + 1\n",
    "        return -1.0j * sum(\n",
    "            exp_sign(exp) * (exp_op(exp) * aux).tr()\n",
    "            for aux, exp in level_1_aux         \n",
    "        )\n",
    "        \n",
    "currM = state_current(fullssM,\"R\")\n",
    "print(currM)\n",
    "   "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 63,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Pade current (0.0008130302805827144+5.421010862427522e-20j)\n",
      "Matsubara current (0.0011018485316349562-0j)\n",
      "Analytical curernt (0.0008130726698759556+0j)\n"
     ]
    }
   ],
   "source": [
    "print(\"Pade current\", currP)\n",
    "print(\"Matsubara current\", currM)\n",
    "print(\"Analytical curernt\", curr_ana)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We see that the Matsubara example is far from converged.\n",
    "Now lets plot the current as a function of bias voltage."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "run time 183.41681957244873\n"
     ]
    }
   ],
   "source": [
    "start=time.time()\n",
    "\n",
    "currPlist = []\n",
    "curranalist = []\n",
    "\n",
    "theta_list = linspace(-4,4,100)\n",
    "\n",
    "for theta in theta_list:\n",
    "    mu_l = theta/2.\n",
    "    mu_r = -theta/2.\n",
    "    #Pade cut-off\n",
    "    lmax = 10\n",
    "\n",
    "\n",
    "\n",
    "\n",
    "    d1 = destroy(2)\n",
    "\n",
    "    e1 = .3\n",
    "\n",
    "\n",
    "    H0 = e1*d1.dag()*d1 \n",
    "\n",
    "\n",
    "    Qops = [d1.dag(),d1,d1.dag(),d1]\n",
    "\n",
    "\n",
    "    rho_0 = basis(2,0)*basis(2,0).dag()\n",
    "\n",
    "    Kk=lmax+1\n",
    "    Ncc = 2\n",
    "\n",
    "    tlist = np.linspace(0,100,1000)\n",
    "\n",
    "\n",
    "    eta_list = [etapR,etamR,etapL,etamL]\n",
    "\n",
    "\n",
    "    gamma_list = [gampR,gammR,gampL,gammL]\n",
    "\n",
    "    resultHEOM = FermionicHEOMSolver(H0, Qops,  eta_list, gamma_list, Ncc)\n",
    "    \n",
    "    rho_0 = basis(2,0)*basis(2,0).dag()\n",
    "    rhossHP,fullssP=resultHEOM.steady_state() \n",
    "\n",
    "    \n",
    "\n",
    "\n",
    "    \n",
    "        #we can extract the current from the auxiliary ADOs calculated in the steady state\n",
    "\n",
    "    aux_1_list_list=[]\n",
    "    aux1_indices_list=[]\n",
    "    aux_2_list_list=[]\n",
    "    aux2_indices_list=[]\n",
    "\n",
    "\n",
    "    K = Kk  \n",
    "\n",
    "    shape = H0.shape[0]\n",
    "    dims = H0.dims\n",
    "\n",
    "\n",
    "\n",
    "    aux_1_list, aux1_indices, idx2state = get_aux_matrices([fullssP], 1, 4, K, Ncc, shape, dims)\n",
    "    aux_2_list, aux2_indices, idx2state = get_aux_matrices([fullssP], 2, 4, K, Ncc, shape, dims)\n",
    "\n",
    "\n",
    "    d1 = destroy(2)   #Kk to 2*Kk\n",
    "    currP = -1.0j * (((sum([(d1*aux_1_list[gg][0]).tr() for gg in range(Kk,2*Kk)]))) - ((sum([(d1.dag()*aux_1_list[gg][0]).tr() for gg in range(Kk)]))))\n",
    "\n",
    "\n",
    "    curr_ana = CurrFunc()\n",
    "    \n",
    "    currPlist.append(currP)\n",
    "    curranalist.append(curr_ana)\n",
    " \n",
    "end=time.time()\n",
    "\n",
    "print(\"run time\", end-start)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 75,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/tmp/ipykernel_5834/1510444643.py:45: DeprecationWarning: Calling np.sum(generator) is deprecated, and in the future will give a different result. Use np.sum(np.fromiter(generator)) or the python sum builtin instead.\n",
      "  return -1.0j * sum(\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "run time 30.83386540412903\n"
     ]
    }
   ],
   "source": [
    "start=time.time()\n",
    "\n",
    "currPlist = []\n",
    "curranalist = []\n",
    "\n",
    "theta_list = linspace(-4,4,100)\n",
    "\n",
    "for theta in theta_list:\n",
    "    mu_l = theta/2.\n",
    "    mu_r = -theta/2.\n",
    "    #Pade cut-off\n",
    "    Nk = 10\n",
    "\n",
    "    d1 = destroy(2)\n",
    "    Q = d1\n",
    "    \n",
    "    \n",
    "\n",
    "\n",
    "    e1 = 0.3\n",
    "\n",
    "\n",
    "    H0 = e1*d1.dag()*d1 \n",
    "\n",
    "    bathL = LorentzianPadeBath(Q,Gamma,W,mu_l,T,Nk,tag=\"L\")\n",
    "    bathR = LorentzianPadeBath(Q,Gamma,W,mu_r,T,Nk,tag=\"R\")\n",
    "        # for a single impurity we converge with max_depth = 2\n",
    "    resultHEOM2 = HEOMSolver(H0, [bathL,bathR], 2, options=options)\n",
    "    \n",
    "    rhossHP,fullssP=resultHEOM2.steady_state() \n",
    "\n",
    "\n",
    "    def state_current(ado_state,bath_tag):\n",
    "        level_1_aux = [\n",
    "            (ado_state.extract(label), ado_state.exps(label)[0])\n",
    "            for label in ado_state.filter(level=1,tags =[bath_tag])\n",
    "        ]\n",
    "        def exp_sign(exp):\n",
    "            return 1 if exp.type == exp.types[\"+\"] else -1\n",
    "\n",
    "        def exp_op(exp):\n",
    "            return exp.Q if exp.type == exp.types[\"+\"] else exp.Q.dag()\n",
    "\n",
    "        k = Nk + 1\n",
    "        return -1.0j * sum(\n",
    "            exp_sign(exp) * (exp_op(exp) * aux).tr()\n",
    "            for aux, exp in level_1_aux         \n",
    "        )\n",
    "\n",
    "    currP = state_current(fullssP,\"R\") \n",
    "    #print(currP)\n",
    "\n",
    "    curr_ana = CurrFunc()\n",
    "    \n",
    "    currPlist.append(currP)\n",
    "    curranalist.append(curr_ana)\n",
    " \n",
    "end=time.time()\n",
    "\n",
    "print(\"run time\", end-start)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 67,
   "metadata": {},
   "outputs": [],
   "source": [
    "matplotlib.rcParams['figure.figsize'] = (7, 5)\n",
    "matplotlib.rcParams['axes.titlesize'] = 25\n",
    "matplotlib.rcParams['axes.labelsize'] = 30\n",
    "matplotlib.rcParams['xtick.labelsize'] = 28\n",
    "matplotlib.rcParams['ytick.labelsize'] = 28\n",
    "matplotlib.rcParams['legend.fontsize'] = 28\n",
    "matplotlib.rcParams['axes.grid'] = False\n",
    "matplotlib.rcParams['savefig.bbox'] = 'tight'\n",
    "matplotlib.rcParams['lines.markersize'] = 5\n",
    "matplotlib.rcParams['font.family'] = 'STIXgeneral' \n",
    "matplotlib.rcParams['mathtext.fontset'] =  'stix'\n",
    "matplotlib.rcParams[\"font.serif\"] = \"STIX\"\n",
    "matplotlib.rcParams['text.usetex'] = False"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 77,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/home/neill/anaconda3/envs/bofinexamples/lib/python3.9/site-packages/matplotlib/cbook/__init__.py:1298: ComplexWarning: Casting complex values to real discards the imaginary part\n",
      "  return np.asarray(x, float)\n",
      "/home/neill/anaconda3/envs/bofinexamples/lib/python3.9/site-packages/matplotlib/cbook/__init__.py:1298: ComplexWarning: Casting complex values to real discards the imaginary part\n",
      "  return np.asarray(x, float)\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 864x504 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig, ax1 = plt.subplots(figsize=(12,7))\n",
    "\n",
    "ax1.plot(theta_list,2.434e-4*1e6*array(curranalist), color=\"black\", linewidth=3, label= r\"Analytical\")\n",
    "ax1.plot(theta_list,2.434e-4*1e6*array(currPlist), 'r--', linewidth=3, label= r\"HEOM $N_k=10$, $n_{\\mathrm{max}}=2$\")\n",
    "\n",
    "\n",
    "ax1.locator_params(axis='y', nbins=4)\n",
    "ax1.locator_params(axis='x', nbins=4)\n",
    "\n",
    "axes.set_xticks([-2.5,0.,2.5])\n",
    "axes.set_xticklabels([-2.5,0,2.5]) \n",
    "ax1.set_xlabel(r\"Bias voltage $\\Delta \\mu$ ($V$)\",fontsize=28)\n",
    "ax1.set_ylabel(r\"Current ($\\mu A$)\",fontsize=28)\n",
    "ax1.legend(fontsize=25)\n",
    "\n",
    "fig.savefig(\"figImpurity.pdf\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
 "metadata": {
  "jupytext": {
   "formats": "ipynb,md:myst"
  },
  "kernelspec": {
   "display_name": "Python 3 (ipykernel)",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.9.7"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 2
}