{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {
    "nbsphinx": "hidden"
   },
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "Starting run with 1 MPI rank(s) at : 2021-01-21 16:24:22.474799\n"
     ]
    }
   ],
   "source": [
    "%matplotlib inline\n",
    "\n",
    "import warnings\n",
    "warnings.filterwarnings('ignore')\n",
    "\n",
    "from triqs.plot.mpl_interface import plt\n",
    "from triqs.gf import Idx\n",
    "from triqs_tprf.plotting_tools import bsplot\n",
    "\n",
    "def plot_delta(delta, lamb):\n",
    "    fig, axs = plt.subplots(figsize=(8, 5), ncols=2)\n",
    "\n",
    "    nw = delta.data.shape[0]\n",
    "    axs[0].plot(range(-nw//2, nw//2), delta[:, :].data[:,500, 0, 0].real *1e3)\n",
    "\n",
    "    axs[0].set_xlabel(r\"$i\\nu_n$\")\n",
    "    axs[0].set_ylabel(r\"$\\Delta$ (meV)\")\n",
    "\n",
    "\n",
    "    im = axs[1].imshow(delta[Idx(0), :].data.reshape(nk, nk).real, cmap=\"RdBu\")\n",
    "    axs[1].set_xticks([])\n",
    "    axs[1].set_yticks([])\n",
    "\n",
    "    axs[1].spines['top'].set_visible(True)\n",
    "    axs[1].spines['right'].set_visible(True)\n",
    "\n",
    "    axs[1].set_xlabel(\"$k_x$\")\n",
    "    axs[1].set_ylabel(\"$k_y$\")\n",
    "\n",
    "    axs[1].text(16, 16, \"$\\Gamma$\", size=20)\n",
    "    axs[1].text(32, 0, \"$M$\", size=20)\n",
    "    axs[1].text(32, 16, \"$X$\", size=20)\n",
    "    \n",
    "    fig.suptitle(r\"$\\lambda = %.3f$\" % lamb, fontsize=20)\n",
    "    \n",
    "\n",
    "def plot_chi(chi_m_wk, chi_d_wk):\n",
    "    path = [(r'$\\Gamma$', 2*np.pi*np.array([0.0, 0.0, 0.0])), \n",
    "            ('X', 2*np.pi*np.array([0.5, 0.0, 0.0])),\n",
    "            ('M', 2*np.pi*np.array([0.5, 0.5, 0.0])), \n",
    "            (r'$\\Gamma$', 2*np.pi*np.array([0.0, 0.0, 0.0])), \n",
    "           ]\n",
    "\n",
    "\n",
    "    ax_bs = plt.subplot(111)\n",
    "\n",
    "    ax_bs.bsplot(chi_m_wk[(Idx(0), slice(None))], path)\n",
    "    ax_bs.bsplot(chi_d_wk[(Idx(0), slice(None))], path)\n",
    "\n",
    "    ax_bs.set_ylabel(r'$\\chi(i\\nu_n=0, \\mathbf{k})$', rotation=0, ha='right')\n",
    "    ax_bs.text(0.62, 0.6, \"$\\chi^{m}$\", transform = ax_bs.transAxes, size=22, color='C0')\n",
    "    ax_bs.text(0.55, 0.18, \"$\\chi^{d}$\", transform = ax_bs.transAxes, size=22, color='C1')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
    "nbsphinx": "hidden"
   },
   "outputs": [],
   "source": [
    "plt.style.use('notebook.mplstyle')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Solving the linearized Eliashberg equation in the random phase approximation limit\n",
    "\n",
    "In this notebook we will walk you through the steps of solving the linearized Eliashberg equation in the random phase approximation (RPA) limit. Make sure, that you have read the [theory](https://triqs.github.io/tprf/latest/theory/eliashberg.html) before reading further.\n",
    "\n",
    "The steps are\n",
    " 1. Construct the density- and magnetic-susceptibilties in RPA\n",
    " 2. Construct the particle-particle vertex in RPA\n",
    " 3. Construct the symmetrizing functions\n",
    " 4. Solve the linearized Eliashberg equation\n",
    "\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 1. Construct the density- and magnetic-susceptibilties in RPA\n",
    "\n",
    "First we need a model and in this example we use the 1-band square lattice."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [],
   "source": [
    "from triqs_tprf.tight_binding import create_square_lattice\n",
    "\n",
    "square_lattice = create_square_lattice(norb=1, t=1.0)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Next we need the non-interacting one-particle Green's function. For this we first create the dispersion relation on a mesh on the Brillouin zone."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [],
   "source": [
    "nk = 32\n",
    "\n",
    "e_k = square_lattice.fourier(square_lattice.get_kmesh((nk, nk, 1)))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "And then we solve the lattice dyson equation `lattice_dyson_g0_wk` for a specific fermionic Matsubara frequency mesh `MeshImFreq` to obtain the non-interacting one-particle Green's function `g0_wk`."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [],
   "source": [
    "from triqs.gf import MeshImFreq\n",
    "from triqs_tprf.lattice import lattice_dyson_g0_wk\n",
    "\n",
    "wmesh = MeshImFreq(beta=10, S='Fermion', n_max=100)\n",
    "g0_wk = lattice_dyson_g0_wk(mu=0, e_k=e_k, mesh=wmesh)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Next we solve for the density- and magnetic-susceptibilties in RPA by first constructing the bare bubble $\\chi_0$ `imtime_bubble_chi0_wk`"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\n",
      "╔╦╗╦═╗╦╔═╗ ╔═╗  ┌┬┐┌─┐┬─┐┌─┐\n",
      " ║ ╠╦╝║║═╬╗╚═╗   │ ├─┘├┬┘├┤ \n",
      " ╩ ╩╚═╩╚═╝╚╚═╝   ┴ ┴  ┴└─└  \n",
      "Two-Particle Response Function tool-box \n",
      "\n",
      "beta  = 10.0\n",
      "nk    = 1024\n",
      "nw    = 200\n",
      "norb  = 1\n",
      "\n",
      "Approx. Memory Utilization: 0.01 GB\n",
      "\n",
      "--> fourier_wk_to_wr\n",
      "--> fourier_wr_to_tr\n",
      "--> chi0_tr_from_grt_PH (bubble in tau & r)\n",
      "--> chi_wr_from_chi_tr\n",
      "--> chi_wk_from_chi_wr (r->k)\n"
     ]
    }
   ],
   "source": [
    "from triqs_tprf.lattice_utils import imtime_bubble_chi0_wk\n",
    "\n",
    "chi0_wk = imtime_bubble_chi0_wk(g0_wk, nw=100)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "and then solving the RPA equations `solve_rpa_PH` for a Hubbard $U$, a rank 4 numpy array."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "from triqs_tprf.lattice import solve_rpa_PH\n",
    "\n",
    "U = 1.0 * np.ones(shape=(1, 1, 1, 1), dtype=complex)\n",
    "\n",
    "chi_d_wk = solve_rpa_PH(chi0_wk, -U) # Minus here for correct density RPA equation\n",
    "chi_m_wk = solve_rpa_PH(chi0_wk, U)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Plotting this over a path through the high-symmetry points looks as follows."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x360 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "dark"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plot_chi(chi_m_wk, chi_d_wk)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 2. Construct the particle-particle vertex in RPA\n",
    "\n",
    "Now we have all the ingredients to build the particle-particle vertex in the RPA limit. In this example we limit us to the singlet particle-particle vertex for a symmetry constraint calculation of the Eliashberg equation.\n",
    "\n",
    "\\begin{align}\n",
    "\\Gamma^{\\mathrm{singlet}}(i\\omega_n, \\mathbf{q})\n",
    "=\n",
    "3\\Phi^{\\mathrm{m}}(i\\omega_n, \\mathbf{q}) - \n",
    "\\Phi^{\\mathrm{d}}(i\\omega_n, \\mathbf{q})\n",
    "+\n",
    "\\frac{1}{2}\n",
    "U^{\\mathrm{d}}\n",
    "+\n",
    "\\frac{3}{2}\n",
    "U^{\\mathrm{m}}\n",
    "\\,\n",
    "\\end{align}\n",
    "\n",
    "where\n",
    "\n",
    "\\begin{align}\n",
    "\\Phi^{\\mathrm{d/m}}(i\\omega_n, \\mathbf{q})\n",
    "=\n",
    "U^{\\mathrm{d/m}}\n",
    "\\chi^{\\mathrm{d/m}}(i\\omega_n, \\mathbf{q})\n",
    "U^{\\mathrm{d/m}}\n",
    "\\,.\n",
    "\\end{align}\n",
    "\n",
    "\n",
    "\n",
    "For the 1-band case $U^{\\mathrm{d/m}}=U$ and we don't have to take correct orbital ording in the products into account, which simplifies everything. But for generality we will show the process which also works for multi-orbital systems, where we first construct the density/magentic reducible ladder vertex $\\Phi^{\\mathrm{d/m}}$ via `construct_phi_wk`."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [],
   "source": [
    "from triqs_tprf.lattice import construct_phi_wk\n",
    "\n",
    "phi_d_wk = construct_phi_wk(chi_d_wk, U)\n",
    "phi_m_wk = construct_phi_wk(chi_m_wk, U)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "And then construct the singlet particle-particle vertex via `construct_gamma_singlet_rpa`."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [],
   "source": [
    "from triqs_tprf.eliashberg import construct_gamma_singlet_rpa\n",
    "\n",
    "gamma_singlet = construct_gamma_singlet_rpa(U, U, phi_d_wk, phi_m_wk)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 3. Construct the symmetrizing functions"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "By using the above $\\Gamma$ we must enforce the allowed $SPOT$ symmetries of the superconducting gap $\\Delta$.\n",
    "Our 1-band model is by default even in orbital symmetry and by using the singlet $\\Gamma$ we are fixing the spin symmetry to odd. We are therefore left with two physical symmetry combinations.\n",
    "\n",
    "| Spin | Parity (Momentum) | Orbital | Time (Frequency) |\n",
    "|:----:|:-----------------:|:-------:|:----------------:|\n",
    "|  odd |        even       |   even  |       even       |\n",
    "|  odd |        odd        |   even  |        odd       |\n",
    "\n",
    "We will solve for them individually, by constructing a symmetrizing function for each of them.\n",
    "We do this by taking `enforce_symmetry` and using `functools.partial` to specifiy the symmetries that we want."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Frequency: Even, Momentum: Even"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [],
   "source": [
    "import functools\n",
    "from triqs_tprf.symmetries import enforce_symmetry\n",
    "\n",
    "variables = [\"frequency\", \"momentum\"]\n",
    "symmetries = [\"even\", \"even\"]\n",
    "\n",
    "symmetrize_freq_even_mom_even = functools.partial(enforce_symmetry, variables=variables, symmetries=symmetries)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Frequency: Odd, Momentum: Odd"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [],
   "source": [
    "symmetries = [\"odd\", \"odd\"]\n",
    "\n",
    "symmetrize_freq_odd_mom_odd = functools.partial(enforce_symmetry, variables=variables, symmetries=symmetries)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 4. Solve the linearized Eliashberg equation"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Now we have everything that we need to solve the linearized Eliashberg equation. \n",
    "We call the `solve_eliashberg` function with each of our `symmetrize_fct`s and solve for the first leading eigenvalue, gap pair (`k=1`)."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [],
   "source": [
    "from triqs_tprf.eliashberg import solve_eliashberg\n",
    "\n",
    "lambdas_freq_even_mom_even, deltas_freq_even_mom_even = solve_eliashberg(gamma_singlet, g0_wk, symmetrize_fct=symmetrize_freq_even_mom_even, k=1)\n",
    "lambdas_freq_odd_mom_odd, deltas_freq_odd_mom_odd = solve_eliashberg(gamma_singlet, g0_wk, symmetrize_fct=symmetrize_freq_odd_mom_odd, k=1)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Plotting them shows that all symmetries are correct and that the gap with even frequency and odd momentum has the higher $\\lambda$ and is therefore leading."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 576x360 with 2 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "dark"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plot_delta(deltas_freq_even_mom_even[0], lambdas_freq_even_mom_even[0])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 576x360 with 2 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "dark"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plot_delta(deltas_freq_odd_mom_odd[0], lambdas_freq_odd_mom_odd[0])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "---"
   ]
  }
 ],
 "metadata": {
  "celltoolbar": "Edit Metadata",
  "kernelspec": {
   "display_name": "Python 3",
   "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": "3.8.5"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 4
}