{
 "cells": [
  {
   "cell_type": "markdown",
   "id": "6a541ac9",
   "metadata": {},
   "source": [
    "# Tutorial\n",
    "\n",
    "Welcome to the `second_quantization` package tutorial! This section contains comprehensive examples demonstrating all the functionality of the package through practical physics applications.\n",
    "\n",
    "```{toctree}\n",
    ":maxdepth: 1\n",
    ":caption: Tutorial Examples\n",
    "```\n",
    "\n",
    "## Tutorial Overview\n",
    "\n",
    "This tutorial consists of three main examples:\n",
    "\n",
    "- **Poor Man's Majorana Model** (this page): A comprehensive example showing symbolic operator algebra, Hamiltonian construction, and spectroscopic analysis\n",
    "- **Parametric Many-Body Model**: Basic usage patterns and simple models\n",
    "- **Quantum Dot Analysis**: Advanced features with realistic condensed matter applications\n",
    "\n",
    "## Examples\n",
    "\n",
    "### Poor Man's Majorana Model\n",
    "\n",
    "#### Overview\n",
    "\n",
    "The \"poor man's Majorana\" model describes a simplified system that can host Majorana-like modes using conventional superconducting quantum dots. This tutorial demonstrates how to use the `second_quantization` package to:\n",
    "\n",
    "1. Define symbolic fermionic operators\n",
    "2. Construct complex many-body Hamiltonians\n",
    "3. Convert symbolic expressions to numerical matrices\n",
    "4. Analyze quantum many-body systems\n",
    "\n",
    "#### System Description\n",
    "\n",
    "We consider a minimal model with two quantum dots (left and right) coupled through a superconducting pairing mechanism. Each dot can host electrons with spin up (↑) and spin down (↓), leading to a four-dimensional single-particle Hilbert space.\n",
    "\n",
    "#### Setting Up the Problem\n",
    "\n",
    "First, let's import the necessary libraries and define our system parameters:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "id": "5059f5f6",
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "import sympy\n",
    "from sympy.physics.quantum.fermion import FermionOp\n",
    "from sympy.physics.quantum import Dagger\n",
    "from sympy.physics.quantum.operatorordering import normal_ordered_form\n",
    "import matplotlib.pyplot as plt\n",
    "\n",
    "# Define operator names for clarity\n",
    "operator_names = [\n",
    "    'c_{L,\\\\uparrow}', 'c_{L,\\\\downarrow}',\n",
    "    'c_{R,\\\\uparrow}', 'c_{R,\\\\downarrow}'\n",
    "]\n",
    "\n",
    "# Define physical parameters as symbolic variables\n",
    "t, theta, Delta, mu_L, mu_R, U, E_z = sympy.symbols(\n",
    "    \"t, theta, Delta, mu_L, mu_R, U, E_z\",\n",
    "    real=True, commutative=True\n",
    ")"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "25ecc11e",
   "metadata": {},
   "source": [
    "Now let's create the fermionic operators for our two-dot system:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "id": "e66df9a9",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Fermionic operators created:\n",
      "  c_{L,\\uparrow}: c_{L,\\uparrow}\n",
      "  c_{L,\\downarrow}: c_{L,\\downarrow}\n",
      "  c_{R,\\uparrow}: c_{R,\\uparrow}\n",
      "  c_{R,\\downarrow}: c_{R,\\downarrow}\n"
     ]
    }
   ],
   "source": [
    "# Create fermionic operators for each site and spin\n",
    "fermions = [FermionOp(name) for name in operator_names]\n",
    "c_Lu, c_Ld, c_Ru, c_Rd = fermions\n",
    "\n",
    "print(\"Fermionic operators created:\")\n",
    "for op, name in zip(fermions, operator_names):\n",
    "    print(f\"  {name}: {op}\")"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "c37d13c6",
   "metadata": {},
   "source": [
    "#### Building the Hamiltonian\n",
    "\n",
    "The poor man's Majorana Hamiltonian consists of several physical terms. Let's construct each term systematically and understand their physical meaning.\n",
    "\n",
    "##### 1. Onsite Energies\n",
    "\n",
    "The onsite energy term describes the chemical potential of electrons on each dot:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "id": "f18a8f5e",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Onsite energy term:\n"
     ]
    },
    {
     "data": {
      "text/latex": [
       "$\\displaystyle \\mu_{L} \\left({{c_{L,\\downarrow}}^\\dagger} {c_{L,\\downarrow}} + {{c_{L,\\uparrow}}^\\dagger} {c_{L,\\uparrow}}\\right) + \\mu_{R} \\left({{c_{R,\\downarrow}}^\\dagger} {c_{R,\\downarrow}} + {{c_{R,\\uparrow}}^\\dagger} {c_{R,\\uparrow}}\\right)$"
      ],
      "text/plain": [
       "mu_L*(Dagger(c_{L,\\downarrow})*c_{L,\\downarrow} + Dagger(c_{L,\\uparrow})*c_{L,\\uparrow}) + mu_R*(Dagger(c_{R,\\downarrow})*c_{R,\\downarrow} + Dagger(c_{R,\\uparrow})*c_{R,\\uparrow})"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Onsite energies (chemical potentials)\n",
    "onsite = mu_L * (Dagger(c_Lu) * c_Lu + Dagger(c_Ld) * c_Ld)\n",
    "onsite += mu_R * (Dagger(c_Ru) * c_Ru + Dagger(c_Rd) * c_Rd)\n",
    "\n",
    "print(\"Onsite energy term:\")\n",
    "display(onsite)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "9ca96fe0",
   "metadata": {},
   "source": [
    "This term allows us to control the occupancy of each dot independently.\n",
    "\n",
    "##### 2. Inter-dot Hopping\n",
    "\n",
    "The hopping term couples the two dots through spin-dependent tunneling:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "id": "91fa2ada",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Hopping term:\n"
     ]
    },
    {
     "data": {
      "text/latex": [
       "$\\displaystyle t \\sin{\\left(\\frac{\\theta}{2} \\right)} \\left({{c_{L,\\downarrow}}^\\dagger} {c_{R,\\uparrow}} - {{c_{L,\\uparrow}}^\\dagger} {c_{R,\\downarrow}}\\right) + t \\cos{\\left(\\frac{\\theta}{2} \\right)} \\left({{c_{L,\\downarrow}}^\\dagger} {c_{R,\\downarrow}} + {{c_{L,\\uparrow}}^\\dagger} {c_{R,\\uparrow}}\\right)$"
      ],
      "text/plain": [
       "t*sin(theta/2)*(Dagger(c_{L,\\downarrow})*c_{R,\\uparrow} - Dagger(c_{L,\\uparrow})*c_{R,\\downarrow}) + t*cos(theta/2)*(Dagger(c_{L,\\downarrow})*c_{R,\\downarrow} + Dagger(c_{L,\\uparrow})*c_{R,\\uparrow})"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\n",
      "Hermitian conjugate:\n"
     ]
    },
    {
     "data": {
      "text/latex": [
       "$\\displaystyle t \\sin{\\left(\\frac{\\theta}{2} \\right)} \\left(- {{c_{R,\\downarrow}}^\\dagger} {c_{L,\\uparrow}} + {{c_{R,\\uparrow}}^\\dagger} {c_{L,\\downarrow}}\\right) + t \\cos{\\left(\\frac{\\theta}{2} \\right)} \\left({{c_{R,\\downarrow}}^\\dagger} {c_{L,\\downarrow}} + {{c_{R,\\uparrow}}^\\dagger} {c_{L,\\uparrow}}\\right)$"
      ],
      "text/plain": [
       "t*sin(theta/2)*(-Dagger(c_{R,\\downarrow})*c_{L,\\uparrow} + Dagger(c_{R,\\uparrow})*c_{L,\\downarrow}) + t*cos(theta/2)*(Dagger(c_{R,\\downarrow})*c_{L,\\downarrow} + Dagger(c_{R,\\uparrow})*c_{L,\\uparrow})"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Hopping between dots with spin-orbit coupling\n",
    "hopping = t * sympy.cos(theta/2) * (Dagger(c_Lu) * c_Ru + Dagger(c_Ld) * c_Rd)\n",
    "hopping += t * sympy.sin(theta/2) * (Dagger(c_Ld) * c_Ru - Dagger(c_Lu) * c_Rd)\n",
    "\n",
    "print(\"Hopping term:\")\n",
    "display(hopping)\n",
    "print(\"\\nHermitian conjugate:\")\n",
    "display(Dagger(hopping))"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "cced65d8",
   "metadata": {},
   "source": [
    "The parameter $\\\\theta$ controls the strength of spin-orbit coupling in the tunneling.\n",
    "\n",
    "##### 3. Superconducting Pairing\n",
    "\n",
    "The pairing term creates Cooper pairs across the two dots:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "id": "44e6cbc8",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Superconducting pairing term:\n"
     ]
    },
    {
     "data": {
      "text/latex": [
       "$\\displaystyle \\Delta \\sin{\\left(\\frac{\\theta}{2} \\right)} \\left({{c_{L,\\downarrow}}^\\dagger} {{c_{R,\\downarrow}}^\\dagger} + {{c_{L,\\uparrow}}^\\dagger} {{c_{R,\\uparrow}}^\\dagger}\\right) + \\Delta \\cos{\\left(\\frac{\\theta}{2} \\right)} \\left({{c_{L,\\downarrow}}^\\dagger} {{c_{R,\\uparrow}}^\\dagger} - {{c_{L,\\uparrow}}^\\dagger} {{c_{R,\\downarrow}}^\\dagger}\\right)$"
      ],
      "text/plain": [
       "Delta*sin(theta/2)*(Dagger(c_{L,\\downarrow})*Dagger(c_{R,\\downarrow}) + Dagger(c_{L,\\uparrow})*Dagger(c_{R,\\uparrow})) + Delta*cos(theta/2)*(Dagger(c_{L,\\downarrow})*Dagger(c_{R,\\uparrow}) - Dagger(c_{L,\\uparrow})*Dagger(c_{R,\\downarrow}))"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\n",
      "Hermitian conjugate:\n"
     ]
    },
    {
     "data": {
      "text/latex": [
       "$\\displaystyle \\Delta \\sin{\\left(\\frac{\\theta}{2} \\right)} \\left({c_{R,\\downarrow}} {c_{L,\\downarrow}} + {c_{R,\\uparrow}} {c_{L,\\uparrow}}\\right) + \\Delta \\cos{\\left(\\frac{\\theta}{2} \\right)} \\left(- {c_{R,\\downarrow}} {c_{L,\\uparrow}} + {c_{R,\\uparrow}} {c_{L,\\downarrow}}\\right)$"
      ],
      "text/plain": [
       "Delta*sin(theta/2)*(c_{R,\\downarrow}*c_{L,\\downarrow} + c_{R,\\uparrow}*c_{L,\\uparrow}) + Delta*cos(theta/2)*(-c_{R,\\downarrow}*c_{L,\\uparrow} + c_{R,\\uparrow}*c_{L,\\downarrow})"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Superconducting pairing term\n",
    "pairing = Delta * sympy.cos(theta/2) * (-Dagger(c_Lu) * Dagger(c_Rd) + Dagger(c_Ld) * Dagger(c_Ru))\n",
    "pairing += Delta * sympy.sin(theta/2) * (Dagger(c_Lu) * Dagger(c_Ru) + Dagger(c_Ld) * Dagger(c_Rd))\n",
    "\n",
    "print(\"Superconducting pairing term:\")\n",
    "display(pairing)\n",
    "print(\"\\nHermitian conjugate:\")\n",
    "display(Dagger(pairing))"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "9dcae6d8",
   "metadata": {},
   "source": [
    "This term enables the formation of Andreev bound states between the dots.\n",
    "\n",
    "##### 4. Zeeman Splitting\n",
    "\n",
    "The Zeeman term splits spin-up and spin-down states in an external magnetic field:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "id": "6a652672",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Zeeman splitting term:\n"
     ]
    },
    {
     "data": {
      "text/latex": [
       "$\\displaystyle E_{z} \\left(- {{c_{L,\\downarrow}}^\\dagger} {c_{L,\\downarrow}} + {{c_{L,\\uparrow}}^\\dagger} {c_{L,\\uparrow}}\\right) + E_{z} \\left(- {{c_{R,\\downarrow}}^\\dagger} {c_{R,\\downarrow}} + {{c_{R,\\uparrow}}^\\dagger} {c_{R,\\uparrow}}\\right)$"
      ],
      "text/plain": [
       "E_z*(-Dagger(c_{L,\\downarrow})*c_{L,\\downarrow} + Dagger(c_{L,\\uparrow})*c_{L,\\uparrow}) + E_z*(-Dagger(c_{R,\\downarrow})*c_{R,\\downarrow} + Dagger(c_{R,\\uparrow})*c_{R,\\uparrow})"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Zeeman splitting in magnetic field\n",
    "zeeman = E_z * (Dagger(c_Lu) * c_Lu - Dagger(c_Ld) * c_Ld)\n",
    "zeeman += E_z * (Dagger(c_Ru) * c_Ru - Dagger(c_Rd) * c_Rd)\n",
    "\n",
    "print(\"Zeeman splitting term:\")\n",
    "display(zeeman)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "2bd024c8",
   "metadata": {},
   "source": [
    "##### 5. Coulomb Interaction\n",
    "\n",
    "The Coulomb interaction penalizes double occupancy on each dot:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "id": "dc4be906",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Coulomb interaction term:\n"
     ]
    },
    {
     "data": {
      "text/latex": [
       "$\\displaystyle U {{c_{L,\\uparrow}}^\\dagger} {c_{L,\\uparrow}} {{c_{L,\\downarrow}}^\\dagger} {c_{L,\\downarrow}} + U {{c_{R,\\uparrow}}^\\dagger} {c_{R,\\uparrow}} {{c_{R,\\downarrow}}^\\dagger} {c_{R,\\downarrow}}$"
      ],
      "text/plain": [
       "U*Dagger(c_{L,\\uparrow})*c_{L,\\uparrow}*Dagger(c_{L,\\downarrow})*c_{L,\\downarrow} + U*Dagger(c_{R,\\uparrow})*c_{R,\\uparrow}*Dagger(c_{R,\\downarrow})*c_{R,\\downarrow}"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Coulomb interaction (double occupancy penalty)\n",
    "coulomb = U * (Dagger(c_Lu) * c_Lu * Dagger(c_Ld) * c_Ld)\n",
    "coulomb += U * (Dagger(c_Ru) * c_Ru * Dagger(c_Rd) * c_Rd)\n",
    "\n",
    "print(\"Coulomb interaction term:\")\n",
    "display(coulomb)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "449d0517",
   "metadata": {},
   "source": [
    "##### 6. Complete Hamiltonian\n",
    "\n",
    "Now we assemble the complete Hamiltonian and put it in normal-ordered form:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "id": "ca1a7363",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Complete Hamiltonian assembled and normal-ordered\n",
      "Number of terms: 26\n"
     ]
    }
   ],
   "source": [
    "# Assemble the complete Hamiltonian\n",
    "H = onsite + zeeman + hopping + Dagger(hopping) + pairing + Dagger(pairing) + coulomb\n",
    "\n",
    "# Convert to normal-ordered form for easier manipulation\n",
    "H = normal_ordered_form(H.expand(), independent=True)\n",
    "\n",
    "print(\"Complete Hamiltonian assembled and normal-ordered\")\n",
    "print(f\"Number of terms: {len(H.args) if hasattr(H, 'args') else 1}\")"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "577b9694",
   "metadata": {},
   "source": [
    "#### Numerical Analysis with `second_quantization`\n",
    "\n",
    "Now we'll convert our symbolic Hamiltonian to a numerical matrix representation using the `second_quantization` package.\n",
    "\n",
    "##### Converting to Matrix Form"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "id": "0e501c92",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Converting symbolic operators to matrix form...\n",
      "Hilbert space dimension: 4\n",
      "Basis states: 4 Fock states\n"
     ]
    }
   ],
   "source": [
    "from second_quantization import hilbert_space\n",
    "\n",
    "# Convert the symbolic Hamiltonian to matrix representation\n",
    "print(\"Converting symbolic operators to matrix form...\")\n",
    "H_matrix_terms = hilbert_space.to_matrix(expression=H, operators=fermions, sparse=False)\n",
    "\n",
    "# Create a callable function for easy parameter substitution\n",
    "H_function = hilbert_space.make_dict_callable(H_matrix_terms)\n",
    "\n",
    "# Get information about the basis\n",
    "basis_ops = hilbert_space.basis_operators(fermions, sparse=False)\n",
    "print(f\"Hilbert space dimension: {len(basis_ops)}\")\n",
    "print(f\"Basis states: {len(basis_ops)} Fock states\")"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "6f147f39",
   "metadata": {},
   "source": [
    "##### Setting Physical Parameters\n",
    "\n",
    "Let's define realistic parameter values for our quantum dot system:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "id": "a46963b8",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "System parameters:\n",
      "  t: 1.0\n",
      "  Delta: 0.5\n",
      "  theta: 0.7853981633974483\n",
      "  mu_L: 0.0\n",
      "  mu_R: 0.0\n",
      "  U: 2.0\n",
      "  E_z: 0.3\n"
     ]
    }
   ],
   "source": [
    "# Define system parameters (energies in units of the hopping t)\n",
    "parameters = {\n",
    "    't': 1.0,          # Hopping energy (reference scale)\n",
    "    'Delta': 0.5,      # Superconducting gap\n",
    "    'theta': np.pi/4,  # Spin-orbit coupling angle\n",
    "    'mu_L': 0.0,       # Left dot chemical potential\n",
    "    'mu_R': 0.0,       # Right dot chemical potential\n",
    "    'U': 2.0,          # Coulomb interaction strength\n",
    "    'E_z': 0.3         # Zeeman energy\n",
    "}\n",
    "\n",
    "print(\"System parameters:\")\n",
    "for param, value in parameters.items():\n",
    "    print(f\"  {param}: {value}\")"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "b25d8207",
   "metadata": {},
   "source": [
    "##### Computing the Spectrum"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "id": "fd33f228",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Eigenvalues (ground state = -1.4374):\n",
      "  State 0: E = -1.4374\n",
      "  State 1: E = -1.3616\n",
      "  State 2: E = -0.8471\n",
      "  State 3: E = -0.7527\n",
      "  State 4: E = -0.0000\n",
      "  State 5: E = 0.1202\n",
      "  State 6: E = 0.3974\n",
      "  State 7: E = 0.7108\n",
      "  State 8: E = 0.9119\n",
      "  State 9: E = 1.0881\n",
      "  State 10: E = 1.6026\n",
      "  State 11: E = 2.0000\n",
      "  State 12: E = 2.8471\n",
      "  State 13: E = 3.1851\n",
      "  State 14: E = 3.3616\n",
      "  State 15: E = 4.1740\n",
      "\n",
      "Energy gap: 0.0758\n",
      "Small gap detected - possible Majorana-like behavior!\n"
     ]
    }
   ],
   "source": [
    "# Evaluate the Hamiltonian matrix with our parameters\n",
    "H_matrix = H_function(**parameters)\n",
    "\n",
    "# Compute eigenvalues and eigenvectors\n",
    "eigenvalues, eigenvectors = np.linalg.eigh(H_matrix)\n",
    "\n",
    "print(f\"Eigenvalues (ground state = {eigenvalues[0]:.4f}):\")\n",
    "for i, E in enumerate(eigenvalues):\n",
    "    print(f\"  State {i}: E = {E:.4f}\")\n",
    "\n",
    "# Check for near-zero modes (potential Majorana signatures)\n",
    "gap = eigenvalues[1] - eigenvalues[0]\n",
    "print(f\"\\nEnergy gap: {gap:.4f}\")\n",
    "if gap < 0.1:\n",
    "    print(\"Small gap detected - possible Majorana-like behavior!\")"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "12bd6d1c",
   "metadata": {},
   "source": [
    "##### Parameter Sweep: Zeeman Field Dependence\n",
    "\n",
    "Let's study how the spectrum changes with the Zeeman field:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "id": "26dbc682",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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      "text/plain": [
       "<Figure size 1000x600 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Minimum gap: 0.0028 at E_z = 0.388\n"
     ]
    }
   ],
   "source": [
    "# Sweep Zeeman field\n",
    "E_z_values = np.linspace(0, 1.0, 50)\n",
    "spectrum = []\n",
    "\n",
    "for Ez in E_z_values:\n",
    "    params_sweep = parameters.copy()\n",
    "    params_sweep['E_z'] = Ez\n",
    "    H_Ez = H_function(**params_sweep)\n",
    "    eigenvals = np.linalg.eigvals(H_Ez)\n",
    "    spectrum.append(np.sort(eigenvals))\n",
    "\n",
    "spectrum = np.array(spectrum)\n",
    "\n",
    "# Plot the energy spectrum\n",
    "plt.figure(figsize=(10, 6))\n",
    "for i in range(len(eigenvalues)):\n",
    "    plt.plot(E_z_values, spectrum[:, i], 'b-', alpha=0.7)\n",
    "\n",
    "plt.xlabel('Zeeman Energy $E_z$')\n",
    "plt.ylabel('Energy')\n",
    "plt.title('Energy Spectrum vs Zeeman Field')\n",
    "plt.grid(True, alpha=0.3)\n",
    "plt.axhline(y=0, color='k', linestyle='--', alpha=0.5)\n",
    "plt.show()\n",
    "\n",
    "# Find potential topological phase transitions\n",
    "gap_values = spectrum[:, 1] - spectrum[:, 0]\n",
    "min_gap_idx = np.argmin(gap_values)\n",
    "print(f\"Minimum gap: {gap_values[min_gap_idx]:.4f} at E_z = {E_z_values[min_gap_idx]:.3f}\")"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "5ac550be",
   "metadata": {},
   "source": [
    "#### Summary\n",
    "\n",
    "This tutorial demonstrated the key features of the `second_quantization` package:\n",
    "\n",
    "1. **Symbolic operator algebra**: We used SymPy's fermionic operators to construct a complex many-body Hamiltonian symbolically.\n",
    "\n",
    "2. **Automatic matrix conversion**: The package automatically converted our symbolic expressions into numerical matrices suitable for computation.\n",
    "\n",
    "3. **Parameter flexibility**: We can easily substitute different parameter values and study the system's behavior.\n",
    "\n",
    "4. **Physical insights**: By analyzing the spectrum, we can identify interesting physics like potential topological phase transitions.\n",
    "\n",
    "The poor man's Majorana model showcases how the package enables rapid exploration of quantum many-body systems, from symbolic construction to numerical analysis."
   ]
  }
 ],
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