{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {
    "deletable": true,
    "editable": true,
    "run_control": {
     "frozen": false,
     "read_only": false
    }
   },
   "source": [
    "# Manipulating fermionic operators\n",
    "\n",
    "Before we see how to use a CTQMC impurity solver, let's learn about operators. Indeed, one of the\n",
    "inputs of the CTQMC solver is a Hamiltonian in operator form.\n",
    "\n",
    "## Fundamental operators\n",
    "\n",
    "After importing the operator module, the keyword `c_dag` and `c` allow to define a new fermionic\n",
    "operator. `c_dag` and `c` are followed by two indices. Inspired by the block structure of Green's functions,\n",
    "the first index is a block index, while the second is the index within the block. Here's an example\n",
    "of operators as they would be defined if we had two blocks *up* and *down* of size 1:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {
    "collapsed": false,
    "deletable": true,
    "editable": true,
    "jupyter": {
     "outputs_hidden": false
    },
    "run_control": {
     "frozen": false,
     "read_only": false
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "1*c_dag('up',0)\n",
      "1*c('up',0)\n",
      "1*c_dag('down',0)\n",
      "1*c('down',0)\n"
     ]
    }
   ],
   "source": [
    "from triqs.operators import c, c_dag, n, Operator # n and Operator will be needed later\n",
    "print(c_dag('up',0))\n",
    "print(c('up',0))\n",
    "print(c_dag('down',0))\n",
    "print(c('down',0))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "deletable": true,
    "editable": true,
    "run_control": {
     "frozen": false,
     "read_only": false
    }
   },
   "source": [
    "## Number operator\n",
    "\n",
    "The keyword `n` is defined as $C^\\dagger C$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
    "collapsed": false,
    "deletable": true,
    "editable": true,
    "jupyter": {
     "outputs_hidden": false
    },
    "run_control": {
     "frozen": false,
     "read_only": false
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "1*c_dag('up',0)*c('up',0)\n"
     ]
    }
   ],
   "source": [
    "print(n('up',0))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "deletable": true,
    "editable": true,
    "run_control": {
     "frozen": false,
     "read_only": false
    }
   },
   "source": [
    "## Operations with operators\n",
    "\n",
    "Operators can be manipulated and anti-commutation relations will be used to simplify\n",
    "expressions"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {
    "collapsed": false,
    "deletable": true,
    "editable": true,
    "jupyter": {
     "outputs_hidden": false
    },
    "run_control": {
     "frozen": false,
     "read_only": false
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "0\n"
     ]
    }
   ],
   "source": [
    "# Should give 0\n",
    "print(n('up',0) - c_dag('up',0)*c('up',0))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {
    "collapsed": false,
    "deletable": true,
    "editable": true,
    "jupyter": {
     "outputs_hidden": false
    },
    "run_control": {
     "frozen": false,
     "read_only": false
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "-1*c_dag('up',0)*c('up',0)\n"
     ]
    }
   ],
   "source": [
    "# Some calculation\n",
    "print(n('up',0) - 2 * c_dag('up',0)*c('up',0))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {
    "collapsed": false,
    "deletable": true,
    "editable": true,
    "jupyter": {
     "outputs_hidden": false
    },
    "run_control": {
     "frozen": false,
     "read_only": false
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "-3*c_dag('down',0)*c('down',0) + -3*c_dag('up',0)*c('up',0) + 4*c_dag('down',0)*c_dag('up',0)*c('up',0)*c('down',0)\n"
     ]
    }
   ],
   "source": [
    "# Define the parameters\n",
    "U = 4\n",
    "mu = 3\n",
    "\n",
    "# H is an empty operator\n",
    "H = Operator()\n",
    "\n",
    "# Add elements to define a Hamiltonian\n",
    "H += U * n('up',0) * n('down',0)\n",
    "H -= mu * (n('up',0) + n('down',0))\n",
    "print(H)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Exact Diagonalization\n",
    "\n",
    "For small system-sizes we can use `AtomDiag` provided by TRIQS to perform exact diagonalization on the Hamiltonian"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Python Library Documentation: function AtomDiag in module triqs.atom_diag\n",
      "\n",
      "AtomDiag(*args, **kwargs)\n",
      "    Construct an exact diagonalization solver, dispatched on the Hamiltonian type.\n",
      "\n",
      "    Returns :class:`AtomDiagReal` when the Hamiltonian (and any further operator\n",
      "    arguments) is purely real, and :class:`AtomDiagComplex` otherwise. The\n",
      "    arguments are forwarded unchanged to the chosen class constructor; see\n",
      "    :class:`AtomDiagReal` for the full list of supported overloads.\n",
      "\n",
      "    Parameters\n",
      "    ----------\n",
      "    h : Operator\n",
      "        Many-body Hamiltonian to be diagonalized.\n",
      "    *args, **kwargs\n",
      "        Additional positional and keyword arguments forwarded to the\n",
      "        :class:`AtomDiagReal` / :class:`AtomDiagComplex` constructor (e.g.\n",
      "        ``fops``, ``hyb``, ``n_min``/``n_max`` or ``qn_vector``).\n",
      "\n",
      "    Returns\n",
      "    -------\n",
      "    AtomDiagReal or AtomDiagComplex\n",
      "        Solved diagonalization problem.\n",
      "\n"
     ]
    }
   ],
   "source": [
    "from triqs.atom_diag import AtomDiag\n",
    "?AtomDiag"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "-3.0\n"
     ]
    }
   ],
   "source": [
    "# List of operator flavors\n",
    "fops = [('up',0), ('down',0)]\n",
    "\n",
    "# Construct AtomDiag object, Performs diagonalization\n",
    "AD = AtomDiag(h=H, fops=fops)\n",
    "\n",
    "print(AD.gs_energy)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We can then use the `AtomDiag` object to obtain for example the atomic Green's functions"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "data": {
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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "from triqs.atom_diag import atomic_g_tau\n",
    "Gtau = atomic_g_tau(atom=AD, beta=10, gf_struct=[('up',1),('down',1)], n_tau=1001)\n",
    "\n",
    "from triqs.plot.mpl_interface import oplot\n",
    "%matplotlib inline\n",
    "oplot(Gtau[\"up\"][0,0].real, name='G')"
   ]
  }
 ],
 "metadata": {
  "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"
  },
  "latex_envs": {
   "LaTeX_envs_menu_present": true,
   "autocomplete": true,
   "bibliofile": "biblio.bib",
   "cite_by": "apalike",
   "current_citInitial": 1,
   "eqLabelWithNumbers": true,
   "eqNumInitial": 1,
   "hotkeys": {
    "equation": "Ctrl-E",
    "itemize": "Ctrl-I"
   },
   "labels_anchors": false,
   "latex_user_defs": false,
   "report_style_numbering": false,
   "user_envs_cfg": false
  },
  "widgets": {
   "state": {},
   "version": "1.1.1"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 4
}