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+{
+ "cells": [
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "# Tutorial: Picket-Fence Model Hamiltonian\n",
+    "\n",
+    "## Introduction\n",
+    "\n",
+    "The **Picket-Fence model** describes a one-dimensional chain of sites (the \"bus\" or \"wire\") where each bus site is coupled to its own isolated \"picket\" site. This creates a comb-like (or picket-fence) topology:\n",
+    "\n",
+    "```\n",
+    "  P0    P1    P2    P3      (picket sites)\n",
+    "  |     |     |     |\n",
+    "  B0 -- B1 -- B2 -- B3      (bus sites)\n",
+    "```\n",
+    "\n",
+    "Each picket site interacts *only* with its corresponding bus site. The bus sites form a linear chain with nearest-neighbor hopping.\n",
+    "\n",
+    "**Why is this model interesting?**\n",
+    "This model introduces controlled localization via side-coupled states, making it ideal for studying the **transport vs. localization crossover**: as the bus–picket coupling $v$ increases, electrons transition from delocalized (metallic) states on the bus chain to localized (insulating) states on isolated dimers.\n",
+    "\n",
+    "### Features demonstrated in this tutorial\n",
+    "\n",
+    "- Defining a custom connectivity matrix for a picket-fence topology\n",
+    "- Mapping between spatial and spin-orbital bases\n",
+    "- Generating 0, 1, and 2-electron integrals in spatial and spin-orbital bases\n",
+    "- Solving for the ground state energy using PySCF FCI (`fci.direct_spin1`)\n",
+    "- Verifying HamHub integral structure against expected picket-fence topology\n",
+    "- **Reduced Hamiltonian verification using the geminal basis**\n",
+    "- Sanity checks at limiting cases ($v_{\\rm ratio} = 0$ and $v_{\\rm ratio} \\to \\infty$)\n",
+    "- **Eigenstate Localization Analysis via Inverse Participation Ratio (IPR)**\n",
+    "- Visualizing the localized ↔ delocalized transition\n",
+    "- Scaling behavior and extensibility of the model\n",
+    "- Saving integrals to `.npz` and `.fcidump` formats"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "## Mathematical Hamiltonian\n",
+    "\n",
+    "We define the Picket-Fence Hamiltonian as:\n",
+    "\n",
+    "\\begin{equation}\n",
+    "\\hat{H} =\n",
+    "\\sum_{i \\in \\text{bus}, \\sigma} t \\, a_{i\\sigma}^\\dagger a_{i+1,\\sigma}\n",
+    "+ \\sum_{i \\in \\text{bus}, \\sigma} v \\, (a_{i\\sigma}^\\dagger a_{p_i\\sigma} + a_{p_i\\sigma}^\\dagger a_{i\\sigma})\n",
+    "+ \\sum_{i,\\sigma} \\epsilon_i \\, \\hat{n}_{i\\sigma}\n",
+    "+ \\sum_i U_i \\, \\hat{n}_{i\\uparrow} \\hat{n}_{i\\downarrow}\n",
+    "\\end{equation}\n",
+    "\n",
+    "where:\n",
+    "\n",
+    "| Parameter | Description |\n",
+    "|---|---|\n",
+    "| $t$ | Bus–bus hopping integral (energy scale). |\n",
+    "| $v$ | Bus–picket coupling strength. |\n",
+    "| $v_{\\text{ratio}} = v/|t|$ | Dimensionless coupling (used in plots). |\n",
+    "| $\\epsilon_i$ | On-site energy of site $i$. |\n",
+    "| $U_i$ | On-site Coulomb repulsion. |\n",
+    "| $p_i$ | Picket site coupled to bus site $i$. |\n",
+    "\n",
+    "This model can be interpreted as a **Hubbard Hamiltonian on a bipartite graph** with constrained connectivity (picket-fence topology).\n",
+    "\n",
+    "For this tutorial, we set:\n",
+    "- Bus–bus hopping: $t = -1$ (sets the energy scale)\n",
+    "- Bus–picket coupling: $v = v_{\\text{ratio}} \\cdot |t|$ (variable)\n",
+    "- On-site energy: $\\varepsilon = 0$ for all sites\n",
+    "- On-site repulsion: $U$ for all sites"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "## Basis Representation\n",
+    "\n",
+    "The `ModelHamiltonian` package operates in two primary bases:\n",
+    "\n",
+    "- **Spatial orbital basis**:\n",
+    "  - Indices: $p, q \\in \\{1, \\ldots, N\\}$\n",
+    "- **Spin-orbital basis**:\n",
+    "  - Indices: $p\\sigma$, where $\\sigma \\in \\{\\alpha, \\beta\\}$\n",
+    "\n",
+    "Mapping rules (see MolKit tutorial):\n",
+    "\n",
+    "$$\n",
+    "h_{pq}^{\\alpha\\alpha} = h_{pq}^{\\beta\\beta} = h_{pq}\n",
+    "$$\n",
+    "\n",
+    "$$\n",
+    "V_{pqrs}^{\\alpha\\alpha\\alpha\\alpha} = V_{pqrs}^{\\text{spatial}}\n",
+    "$$\n",
+    "\n",
+    "Mixed-spin terms vanish:\n",
+    "$$\n",
+    "V^{\\alpha\\beta} = 0\n",
+    "$$"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "## 1. Setup and Imports"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 14,
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "import numpy as np\n",
+    "import matplotlib.pyplot as plt\n",
+    "from pyscf import fci\n",
+    "from moha import HamHub\n",
+    "from moha.molkit.hamiltonians import MolHam\n",
+    "from moha.molkit.utils.tools import to_geminal\n",
+    "import warnings\n",
+    "\n",
+    "warnings.filterwarnings(\"ignore\")\n",
+    "np.set_printoptions(precision=4, suppress=True)"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "## 2. Defining the Picket-Fence Connectivity\n",
+    "\n",
+    "We build a picket-fence system with `N_bus = 4` bus sites and 4 picket sites (total 8 sites).\n",
+    "\n",
+    "The connectivity matrix is an $8 \\times 8$ symmetric matrix constructed as follows:\n",
+    "\n",
+    "- **Bus chain:** Sites $0, 1, 2, 3$ are connected with nearest-neighbor hopping amplitude 1.\n",
+    "- **Bus–picket coupling:** Each bus site $i$ is coupled to picket site $i + N_{\\text{bus}}$ with amplitude $v_{\\text{ratio}}$.\n",
+    "- **Picket sites** (4, 5, 6, 7) have **no** connections to each other.\n",
+    "\n",
+    "The connectivity matrix fully defines the graph structure of the Hamiltonian — `HamHub` reads this matrix and automatically constructs the hopping terms $h_{pq} = \\beta \\cdot c_{pq}$ (where $c_{pq}$ is the matrix entry), so no manual term construction is needed."
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 15,
+   "metadata": {},
+   "outputs": [
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "Connectivity matrix (v_ratio = 0.5):\n",
+      "[[0.  1.  0.  0.  0.5 0.  0.  0. ]\n",
+      " [1.  0.  1.  0.  0.  0.5 0.  0. ]\n",
+      " [0.  1.  0.  1.  0.  0.  0.5 0. ]\n",
+      " [0.  0.  1.  0.  0.  0.  0.  0.5]\n",
+      " [0.5 0.  0.  0.  0.  0.  0.  0. ]\n",
+      " [0.  0.5 0.  0.  0.  0.  0.  0. ]\n",
+      " [0.  0.  0.5 0.  0.  0.  0.  0. ]\n",
+      " [0.  0.  0.  0.5 0.  0.  0.  0. ]]\n"
+     ]
+    }
+   ],
+   "source": [
+    "def build_picket_fence_connectivity(N_bus, v_ratio=1.0):\n",
+    "    \"\"\"Build the connectivity matrix for a picket-fence system.\n",
+    "\n",
+    "    Parameters\n",
+    "    ----------\n",
+    "    N_bus : int\n",
+    "        Number of bus sites.\n",
+    "    v_ratio : float\n",
+    "        Dimensionless bus-picket coupling v / |t|.\n",
+    "\n",
+    "    Returns\n",
+    "    -------\n",
+    "    np.ndarray\n",
+    "        Connectivity matrix of shape (2*N_bus, 2*N_bus).\n",
+    "    \"\"\"\n",
+    "    N_total = 2 * N_bus\n",
+    "    conn = np.zeros((N_total, N_total))\n",
+    "    # Bus chain: nearest-neighbor connections (amplitude = 1)\n",
+    "    for i in range(N_bus - 1):\n",
+    "        conn[i, i + 1] = conn[i + 1, i] = 1.0\n",
+    "    # Bus-picket coupling (amplitude = v_ratio)\n",
+    "    for i in range(N_bus):\n",
+    "        conn[i, i + N_bus] = conn[i + N_bus, i] = v_ratio\n",
+    "    return conn\n",
+    "\n",
+    "N_bus = 4\n",
+    "v_ratio = 0.5  # dimensionless: v / |t|\n",
+    "\n",
+    "conn = build_picket_fence_connectivity(N_bus, v_ratio=v_ratio)\n",
+    "print(\"Connectivity matrix (v_ratio = 0.5):\")\n",
+    "print(conn)"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "## 3. Instantiating the Hamiltonian\n",
+    "\n",
+    "We use the `HamHub` (Hubbard) class from the Model Hamiltonian package. The connectivity matrix fully encodes the picket-fence topology.\n",
+    "\n",
+    "**Parameters:**\n",
+    "- `alpha = 0`: on-site energy $\\varepsilon_i = 0$ for all sites\n",
+    "- `beta = -1`: sets the energy scale for the hopping (the connectivity matrix entries scale $\\beta$)\n",
+    "- `u_onsite`: on-site Coulomb repulsion $U$ for each site\n",
+    "\n",
+    "The resulting one-body matrix entries are:\n",
+    "\n",
+    "$$h_{pq} = \\alpha \\, \\delta_{pq} + \\beta \\cdot c_{pq}$$\n",
+    "\n",
+    "where $c_{pq}$ is the connectivity matrix value."
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 16,
+   "metadata": {},
+   "outputs": [
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "Number of sites: 8\n",
+      "System: 4 bus sites + 4 picket sites = 8 total sites\n"
+     ]
+    }
+   ],
+   "source": [
+    "N_total = 2 * N_bus\n",
+    "U_val = 2.0  # on-site Coulomb repulsion\n",
+    "\n",
+    "ham_hub = HamHub(\n",
+    "    connectivity=conn,\n",
+    "    alpha=0,\n",
+    "    beta=-1,\n",
+    "    u_onsite=np.full(N_total, U_val),\n",
+    ")\n",
+    "\n",
+    "print(f\"Number of sites: {ham_hub.n_sites}\")\n",
+    "print(f\"System: {N_bus} bus sites + {N_bus} picket sites = {N_total} total sites\")"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "## 4. Generating Integrals\n",
+    "\n",
+    "The Model Hamiltonian package generates 0-, 1-, and 2-electron integrals. These can be obtained in either the **spatial** or **spin-orbital** basis.\n",
+    "\n",
+    "### 4.1 Zero-body integral (energy shift)"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 17,
+   "metadata": {},
+   "outputs": [
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "Zero-body integral (energy shift): 0\n"
+     ]
+    }
+   ],
+   "source": [
+    "e0 = ham_hub.generate_zero_body_integral()\n",
+    "print(f\"Zero-body integral (energy shift): {e0}\")"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "### 4.2 One-body integrals\n",
+    "\n",
+    "The one-body integral matrix $h_{pq}$ encodes the hopping terms and on-site energies."
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 18,
+   "metadata": {},
+   "outputs": [
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "One-body integrals (spatial basis):\n",
+      "  Shape: (8, 8)\n",
+      "[[ 0.  -1.   0.   0.  -0.5  0.   0.   0. ]\n",
+      " [-1.   0.  -1.   0.   0.  -0.5  0.   0. ]\n",
+      " [ 0.  -1.   0.  -1.   0.   0.  -0.5  0. ]\n",
+      " [ 0.   0.  -1.   0.   0.   0.   0.  -0.5]\n",
+      " [-0.5  0.   0.   0.   0.   0.   0.   0. ]\n",
+      " [ 0.  -0.5  0.   0.   0.   0.   0.   0. ]\n",
+      " [ 0.   0.  -0.5  0.   0.   0.   0.   0. ]\n",
+      " [ 0.   0.   0.  -0.5  0.   0.   0.   0. ]]\n",
+      "\n",
+      "------------------------------------------------------------\n",
+      "\n",
+      "One-body integrals (spin-orbital basis):\n",
+      "  Shape: (16, 16)\n"
+     ]
+    }
+   ],
+   "source": [
+    "# Spatial basis\n",
+    "h1_spatial = ham_hub.generate_one_body_integral(dense=True, basis='spatial basis')\n",
+    "print(\"One-body integrals (spatial basis):\")\n",
+    "print(f\"  Shape: {h1_spatial.shape}\")\n",
+    "print(h1_spatial)\n",
+    "\n",
+    "print(\"\\n\" + \"-\" * 60 + \"\\n\")\n",
+    "\n",
+    "# Spin-orbital basis\n",
+    "h1_spin = ham_hub.generate_one_body_integral(dense=True, basis='spinorbital basis')\n",
+    "print(\"One-body integrals (spin-orbital basis):\")\n",
+    "print(f\"  Shape: {h1_spin.shape}\")"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "### 4.3 Two-body integrals\n",
+    "\n",
+    "The two-body integral tensor $V_{pqrs}$ encodes the electron–electron repulsion."
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 19,
+   "metadata": {},
+   "outputs": [
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "Two-body integrals (spatial basis):\n",
+      "  Shape: (8, 8, 8, 8)\n",
+      "\n",
+      "------------------------------------------------------------\n",
+      "\n",
+      "Two-body integrals (spin-orbital basis):\n",
+      "  Shape: (16, 16, 16, 16)\n"
+     ]
+    }
+   ],
+   "source": [
+    "# Spatial basis with 4-fold symmetry\n",
+    "h2_spatial = ham_hub.generate_two_body_integral(dense=True, basis='spatial basis', sym=4)\n",
+    "print(\"Two-body integrals (spatial basis):\")\n",
+    "print(f\"  Shape: {h2_spatial.shape}\")\n",
+    "\n",
+    "print(\"\\n\" + \"-\" * 60 + \"\\n\")\n",
+    "\n",
+    "# Spin-orbital basis with 4-fold symmetry\n",
+    "h2_spin = ham_hub.generate_two_body_integral(dense=True, basis='spinorbital basis', sym=4)\n",
+    "print(\"Two-body integrals (spin-orbital basis):\")\n",
+    "print(f\"  Shape: {h2_spin.shape}\")"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "## 5. FCI Ground State Solver\n",
+    "\n",
+    "### Integral Convention\n",
+    "\n",
+    "- `ModelHamiltonian` outputs **physicists' notation** $\\langle p q | r s\\rangle$\n",
+    "- `PySCF` expects **chemists' notation** $(p r | q s)$\n",
+    "\n",
+    "Transformation:\n",
+    "$$\n",
+    "V_{\\text{phys}}(p,q,r,s) \\rightarrow V_{\\text{chem}}(p,r,q,s)\n",
+    "$$"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 20,
+   "metadata": {},
+   "outputs": [
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "FCI ground state energy (v_ratio=0.5): -4.5579753175\n"
+     ]
+    }
+   ],
+   "source": [
+    "def solve_fci(h1, h2, norb, nelec, ecore=0.0):\n",
+    "    \"\"\"Solve the FCI problem using PySCF's fci.direct_spin1.\n",
+    "\n",
+    "    Converts integrals from physicists' to chemists' notation before calling\n",
+    "    the solver: V_chem(p, r, q, s) = V_phys(p, q, r, s).\n",
+    "    \"\"\"\n",
+    "    h2_chem = np.einsum('pqrs -> prqs', h2)\n",
+    "    e, ci_vec = fci.direct_spin1.kernel(h1, h2_chem, norb, nelec, ecore=ecore, tol=1e-12)\n",
+    "    return e, ci_vec\n",
+    "\n",
+    "N_elec = N_total  # half-filling: one electron per site\n",
+    "nelec = (N_elec // 2, N_elec // 2)  # (n_alpha, n_beta)\n",
+    "\n",
+    "# Use the spatial-basis integrals\n",
+    "h1 = h1_spatial\n",
+    "h2 = h2_spatial\n",
+    "\n",
+    "e_fci_moha, ci_vec = solve_fci(h1, h2, N_total, nelec, ecore=e0)\n",
+    "print(f\"FCI ground state energy (v_ratio={v_ratio}): {e_fci_moha:.10f}\")"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "## 6. Verifying the Integral Structure\n",
+    "\n",
+    "We verify that `HamHub` produced the correct one-body matrix by checking its matrix elements against the expected picket-fence topology.\n",
+    "\n",
+    "For a system with `beta=-1` and `alpha=0`, the formula $h_{pq} = \\alpha\\,\\delta_{pq} + \\beta \\cdot c_{pq}$ gives:\n",
+    "\n",
+    "| Bond type | Connectivity value | Expected $h_{pq}$ |\n",
+    "|---|---|---|\n",
+    "| Bus–bus | $c_{i,i+1} = 1$ | $\\beta \\cdot 1 = -1$ |\n",
+    "| Bus–picket | $c_{i,i+N_{\\text{bus}}} = v_{\\text{ratio}}$ | $\\beta \\cdot v_{\\text{ratio}} = -0.5$ |\n",
+    "| On-site | $\\alpha = 0$ | $0$ |"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 21,
+   "metadata": {},
+   "outputs": [
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "Bus-chain hopping values:   [np.float64(-1.0), np.float64(-1.0), np.float64(-1.0)]\n",
+      "  Expected: -1.0  ✔\n",
+      "Bus-picket coupling values: [np.float64(-0.5), np.float64(-0.5), np.float64(-0.5), np.float64(-0.5)]\n",
+      "  Expected: -0.5  ✔\n",
+      "Diagonal (on-site) values:  [0. 0. 0. 0. 0. 0. 0. 0.]\n",
+      "  Expected: 0.0  ✔\n",
+      "\n",
+      "All structural checks PASSED.\n"
+     ]
+    }
+   ],
+   "source": [
+    "beta = -1.0\n",
+    "\n",
+    "# Verify bus chain hoppings\n",
+    "bus_hoppings = [h1[i, i+1] for i in range(N_bus - 1)]\n",
+    "expected_bus = beta * 1.0\n",
+    "print(f\"Bus-chain hopping values:   {bus_hoppings}\")\n",
+    "assert all(np.isclose(v, expected_bus) for v in bus_hoppings)\n",
+    "print(f\"  Expected: {expected_bus}  ✔\")\n",
+    "\n",
+    "# Verify bus-picket couplings\n",
+    "pic_hoppings = [h1[i, i + N_bus] for i in range(N_bus)]\n",
+    "expected_pic = beta * v_ratio\n",
+    "print(f\"Bus-picket coupling values: {pic_hoppings}\")\n",
+    "assert all(np.isclose(v, expected_pic) for v in pic_hoppings)\n",
+    "print(f\"  Expected: {expected_pic}  ✔\")\n",
+    "\n",
+    "# Verify diagonal (on-site energies)\n",
+    "diag_vals = np.diag(h1)\n",
+    "print(f\"Diagonal (on-site) values:  {diag_vals}\")\n",
+    "assert np.allclose(diag_vals, 0.0)\n",
+    "print(f\"  Expected: 0.0  ✔\")\n",
+    "\n",
+    "print(\"\\nAll structural checks PASSED.\")"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "## 7. Reduced Hamiltonian & Geminal Verification\n",
+    "\n",
+    "We use the `MolHam` class to verify the consistency between spin-orbital and geminal representations. The reduced Hamiltonian $k_{pqrs}$ encapsulates both one- and two-body terms into a single 4-index tensor.\n",
+    "\n",
+    "### Formula\n",
+    "$$\n",
+    "k_{pqrs} = \\frac{1}{2(N-1)} \\left( h_{pq} \\delta_{rs} + h_{rs} \\delta_{pq} \\right) + \\frac{1}{2} V_{pqrs}\n",
+    "$$"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 22,
+   "metadata": {},
+   "outputs": [
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "E_spin-orbital: -4.5579753175\n",
+      "E_geminal:      -4.5579753175\n",
+      "FCI electronic energy: -4.5579753175\n",
+      "Consistency check PASSED: E_spin == E_gem == E_electronic\n"
+     ]
+    }
+   ],
+   "source": [
+    "# Wrap integrals in MolHam object\n",
+    "hami = MolHam(one_body=h1, two_body=h2, zero_body=e0)\n",
+    "\n",
+    "# Obtain RDMs from FCI wavefunction\n",
+    "rdm1s, rdm2s = fci.direct_spin1.make_rdm12s(ci_vec, N_total, nelec)\n",
+    "\n",
+    "# Construct spin-orbital RDM2 in physicists' notation\n",
+    "rdm2_spin = np.zeros((2 * N_total, 2 * N_total, 2 * N_total, 2 * N_total))\n",
+    "for i in range(N_total):\n",
+    "    for j in range(N_total):\n",
+    "        for k in range(N_total):\n",
+    "            for l in range(N_total):\n",
+    "                rdm2_spin[i, j, k, l] = rdm2s[0][i, k, j, l]  # aaaa\n",
+    "                rdm2_spin[i+N_total, j+N_total, k+N_total, l+N_total] = rdm2s[2][i, k, j, l]  # bbbb\n",
+    "                rdm2_spin[i, j+N_total, k, l+N_total] = rdm2s[1][i, k, j, l]  # abab\n",
+    "                rdm2_spin[i+N_total, j, k+N_total, l] = rdm2s[1][i, k, j, l]  # baba\n",
+    "\n",
+    "# 1. Compute energy using spin-orbital basis\n",
+    "H_reduced = hami.to_reduced(n_elec=sum(nelec))\n",
+    "E_spin = np.sum(H_reduced * rdm2_spin)\n",
+    "\n",
+    "# 2. Compute energy using geminal basis\n",
+    "H_gem = to_geminal(H_reduced, type='h2')\n",
+    "rdm_gem = to_geminal(rdm2_spin, type='rdm2')\n",
+    "E_gem = np.einsum('pq,pq', H_gem, rdm_gem)\n",
+    "\n",
+    "print(f\"E_spin-orbital: {E_spin:.10f}\")\n",
+    "print(f\"E_geminal:      {E_gem:.10f}\")\n",
+    "print(f\"FCI electronic energy: {e_fci_moha - e0:.10f}\")\n",
+    "assert np.allclose(E_spin, E_gem)\n",
+    "assert np.allclose(E_spin, e_fci_moha - e0)\n",
+    "print(\"Consistency check PASSED: E_spin == E_gem == E_electronic\")"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "## 8. Sanity Check: Limiting Cases\n",
+    "\n",
+    "Before running the full sweep, we verify the two limiting behaviors of the model at half-filling:\n",
+    "\n",
+    "| Limit | Physical picture | Expected behavior |\n",
+    "|---|---|---|\n",
+    "| $v_{\\text{ratio}} \\to 0$ | Pickets decouple; system → pure $N_{\\text{bus}}$-site chain | Energy dominated by bus chain; pickets carry zero hopping |\n",
+    "| $v_{\\text{ratio}} \\to \\infty$ | Bus–bus hopping negligible; system → $N_{\\text{bus}}$ independent dimers | $E \\to N_{\\text{bus}} \\times E_{\\text{dimer}}(v_{\\text{ratio}})$ |\n",
+    "\n",
+    "Both checks use the **full 8-site system** with 8 electrons (half-filling), ensuring consistent comparison."
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 23,
+   "metadata": {},
+   "outputs": [
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "Limit v_ratio → 0 (v_ratio = 1e-06):\n",
+      "  Full system energy:   -2.596722\n",
+      "\n",
+      "Limit v_ratio → ∞ (v_ratio = 8.0):\n",
+      "  Full system energy:        -62.218092\n",
+      "  N_bus × single dimer:      -62.031242\n",
+      "  Relative difference:       0.3003%\n",
+      "\n",
+      "Interpretation:\n",
+      "  At v_ratio=1e-06: purely bus-dominated; pickets are inert.\n",
+      "  At v_ratio=8.0: system ≈ 4 independent dimers (relative error = 0.30%).\n"
+     ]
+    }
+   ],
+   "source": [
+    "# ---------------------------------------------------------------\n",
+    "# Limit 1: v_ratio → 0 (pickets decouple from bus)\n",
+    "# ---------------------------------------------------------------\n",
+    "# At v_ratio=0, the 8-site system splits into:\n",
+    "#   - A 4-site bus chain with 4 electrons\n",
+    "#   - 4 isolated picket sites with 4 electrons (1 per site → 0 kinetic energy)\n",
+    "# Full energy = E_bus + E_pickets = E_bus + 0 (no hopping on isolated sites)\n",
+    "# We verify by checking energy at a very small v_ratio.\n",
+    "\n",
+    "eps = 1e-6  # effectively zero coupling\n",
+    "conn_eps = build_picket_fence_connectivity(N_bus, v_ratio=eps)\n",
+    "hub_eps = HamHub(connectivity=conn_eps, alpha=0, beta=-1, u_onsite=np.full(N_total, U_val))\n",
+    "e_eps, _ = solve_fci(\n",
+    "    hub_eps.generate_one_body_integral(dense=True, basis='spatial basis'),\n",
+    "    hub_eps.generate_two_body_integral(dense=True, basis='spatial basis', sym=4),\n",
+    "    N_total, nelec, ecore=hub_eps.generate_zero_body_integral()\n",
+    ")\n",
+    "\n",
+    "# ---------------------------------------------------------------\n",
+    "# Limit 2: v_ratio → ∞ (strong dimer formation)\n",
+    "# ---------------------------------------------------------------\n",
+    "# At large v_ratio, the system → N_bus independent 2-site dimers.\n",
+    "# Each dimer: 1 bus site + 1 picket, with coupling v = beta * v_ratio.\n",
+    "# We compute the energy of ONE such dimer (2 sites, 2 electrons, 1↑+1↓)\n",
+    "# using the SAME v_ratio and compare N_bus × E_dimer to the full system.\n",
+    "\n",
+    "v_large = 8.0\n",
+    "\n",
+    "# Full 8-site system at v_large\n",
+    "conn_large = build_picket_fence_connectivity(N_bus, v_ratio=v_large)\n",
+    "hub_large = HamHub(connectivity=conn_large, alpha=0, beta=-1, u_onsite=np.full(N_total, U_val))\n",
+    "e_large, _ = solve_fci(\n",
+    "    hub_large.generate_one_body_integral(dense=True, basis='spatial basis'),\n",
+    "    hub_large.generate_two_body_integral(dense=True, basis='spatial basis', sym=4),\n",
+    "    N_total, nelec, ecore=hub_large.generate_zero_body_integral()\n",
+    ")\n",
+    "\n",
+    "# Single dimer: 2-site system with coupling v_large (bus-picket bond only)\n",
+    "conn_dimer = np.array([[0, v_large], [v_large, 0]], dtype=float)\n",
+    "hub_dimer = HamHub(connectivity=conn_dimer, alpha=0, beta=-1, u_onsite=np.full(2, U_val))\n",
+    "e_dimer, _ = solve_fci(\n",
+    "    hub_dimer.generate_one_body_integral(dense=True, basis='spatial basis'),\n",
+    "    hub_dimer.generate_two_body_integral(dense=True, basis='spatial basis', sym=4),\n",
+    "    2, (1, 1), ecore=hub_dimer.generate_zero_body_integral()\n",
+    ")\n",
+    "\n",
+    "print(f\"Limit v_ratio → 0 (v_ratio = {eps}):\")\n",
+    "print(f\"  Full system energy:   {e_eps:.6f}\")\n",
+    "print()\n",
+    "print(f\"Limit v_ratio → ∞ (v_ratio = {v_large}):\")\n",
+    "print(f\"  Full system energy:        {e_large:.6f}\")\n",
+    "print(f\"  N_bus × single dimer:      {N_bus * e_dimer:.6f}\")\n",
+    "print(f\"  Relative difference:       {abs(e_large - N_bus * e_dimer) / abs(e_large):.4%}\")\n",
+    "print()\n",
+    "print(f\"Interpretation:\")\n",
+    "print(f\"  At v_ratio={eps}: purely bus-dominated; pickets are inert.\")\n",
+    "print(f\"  At v_ratio={v_large}: system ≈ {N_bus} independent dimers \"\n",
+    "      f\"(relative error = {abs(e_large - N_bus * e_dimer) / abs(e_large):.2%}).\")"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "## 9. Eigenstate Localization Analysis via IPR\n",
+    "\n",
+    "### Objective\n",
+    "\n",
+    "We quantify the localization–delocalization transition by analyzing the single-particle density matrix and computing the **Inverse Participation Ratio (IPR)**.\n",
+    "\n",
+    "### Key Idea\n",
+    "\n",
+    "For a set of normalized site occupations $\\{n_i\\}$ (diagonal of the 1-RDM), define:\n",
+    "\n",
+    "$$\n",
+    "\\text{IPR} = \\sum_i n_i^2 \\qquad \\text{where } \\sum_i n_i = 1\n",
+    "$$\n",
+    "\n",
+    "| IPR value | Physical meaning |\n",
+    "|---|---|\n",
+    "| $\\text{IPR} \\approx 1/N$ | Fully delocalized: electrons spread uniformly across all $N$ sites |\n",
+    "| $\\text{IPR} \\to 1$ | Strongly localized: one site dominates the occupation |\n",
+    "\n",
+    "In the picket-fence model:\n",
+    "- Small $v_{\\text{ratio}}$: electrons are delocalized across the bus chain → low IPR\n",
+    "- Large $v_{\\text{ratio}}$: electrons localize onto bus–picket dimers → IPR rises"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 24,
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "def compute_ipr(rdm1):\n",
+    "    \"\"\"Compute IPR from the 1-body density matrix (alpha block).\n",
+    "\n",
+    "    Uses diagonal site occupations as proxy for localization.\n",
+    "\n",
+    "    Parameters\n",
+    "    ----------\n",
+    "    rdm1 : np.ndarray\n",
+    "        1-body density matrix (N x N).\n",
+    "\n",
+    "    Returns\n",
+    "    -------\n",
+    "    float\n",
+    "        Inverse Participation Ratio.\n",
+    "    \"\"\"\n",
+    "    occ = np.diag(rdm1)\n",
+    "    occ = occ / np.sum(occ)  # normalize to sum = 1\n",
+    "    return np.sum(occ ** 2)\n",
+    "\n",
+    "\n",
+    "v_values = np.linspace(0.1, 3.0, 30)\n",
+    "ipr_values = []\n",
+    "\n",
+    "for v in v_values:\n",
+    "    c = build_picket_fence_connectivity(N_bus, v_ratio=v)\n",
+    "    h_ipr = HamHub(connectivity=c, alpha=0, beta=-1, u_onsite=np.full(N_total, U_val))\n",
+    "    h1_ipr = h_ipr.generate_one_body_integral(dense=True, basis='spatial basis')\n",
+    "    h2_ipr = h_ipr.generate_two_body_integral(dense=True, basis='spatial basis', sym=4)\n",
+    "    _, ci_v = solve_fci(h1_ipr, h2_ipr, N_total, nelec,\n",
+    "                        ecore=h_ipr.generate_zero_body_integral())\n",
+    "    rdm1_v, _ = fci.direct_spin1.make_rdm12s(ci_v, N_total, nelec)\n",
+    "    ipr_values.append(compute_ipr(rdm1_v[0]))  # alpha block\n",
+    "\n",
+    "ipr_values = np.array(ipr_values)"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 25,
+   "metadata": {},
+   "outputs": [
+    {
+     "data": {
+      "image/png": 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",
+      "text/plain": [
+       "<Figure size 1560x650 with 2 Axes>"
+      ]
+     },
+     "metadata": {},
+     "output_type": "display_data"
+    },
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "IPR bounds:\n",
+      "  Uniform delocalization reference (1/N): 0.1250\n",
+      "  IPR at v_ratio=0.1:                     0.1544\n",
+      "  IPR at v_ratio=3.0:                     0.1250\n"
+     ]
+    }
+   ],
+   "source": [
+    "fig, axes = plt.subplots(1, 2, figsize=(12, 5), dpi=130)\n",
+    "\n",
+    "# Panel 1: IPR vs coupling\n",
+    "axes[0].plot(v_values, ipr_values, 'o-', linewidth=2, markersize=5, color='steelblue')\n",
+    "axes[0].axhline(1 / N_total, linestyle='--', color='gray', label=r'$1/N$ (delocalized)')\n",
+    "axes[0].set_xlabel(r'Coupling Strength $v_{\\rm ratio} = v/|t|$', fontsize=12)\n",
+    "axes[0].set_ylabel('IPR', fontsize=12)\n",
+    "axes[0].set_title('Localization Transition\\n(Picket-Fence Model)', fontsize=12)\n",
+    "axes[0].legend(fontsize=11)\n",
+    "axes[0].grid(True, linestyle='--', alpha=0.4)\n",
+    "\n",
+    "# Panel 2: IPR interpretation zones\n",
+    "delocalized_ref = 1 / N_total\n",
+    "threshold = (delocalized_ref + ipr_values.max()) / 2\n",
+    "axes[1].plot(v_values, ipr_values, 'o-', linewidth=2, markersize=5, color='steelblue')\n",
+    "axes[1].axhspan(0, threshold, alpha=0.1, color='green', label='More delocalized')\n",
+    "axes[1].axhspan(threshold, ipr_values.max() + 0.01, alpha=0.1, color='red', label='More localized')\n",
+    "axes[1].set_xlabel(r'Coupling Strength $v_{\\rm ratio} = v/|t|$', fontsize=12)\n",
+    "axes[1].set_ylabel('IPR', fontsize=12)\n",
+    "axes[1].set_title('Regimes of Localization', fontsize=12)\n",
+    "axes[1].legend(fontsize=10)\n",
+    "axes[1].grid(True, linestyle='--', alpha=0.4)\n",
+    "\n",
+    "plt.tight_layout()\n",
+    "plt.show()\n",
+    "\n",
+    "print(f\"IPR bounds:\")\n",
+    "print(f\"  Uniform delocalization reference (1/N): {1/N_total:.4f}\")\n",
+    "print(f\"  IPR at v_ratio=0.1:                     {ipr_values[0]:.4f}\")\n",
+    "print(f\"  IPR at v_ratio=3.0:                     {ipr_values[-1]:.4f}\")"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "### Physical Insight\n",
+    "\n",
+    "- **Small $v_{\\text{ratio}}$:** IPR is small → electrons are spread across the bus → **delocalized / metallic regime**.\n",
+    "- **Large $v_{\\text{ratio}}$:** IPR increases → electrons localize on bus–picket dimers → **insulating / localized regime**.\n",
+    "\n",
+    "**Key result:** The picket-fence model exhibits a **continuous localization crossover** controlled by the dimensionless side-coupling strength $v_{\\text{ratio}} = v/|t|$. This makes it a tractable model for studying transport vs. localization physics in quasi-1D systems."
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "## 10. Visualization: Ground State Energy vs. Coupling Strength\n",
+    "\n",
+    "We sweep $v_{\\text{ratio}}$ and compute the FCI ground state energy at each value."
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 26,
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "energies = []\n",
+    "\n",
+    "for v in v_values:\n",
+    "    c = build_picket_fence_connectivity(N_bus, v_ratio=v)\n",
+    "    h = HamHub(connectivity=c, alpha=0, beta=-1, u_onsite=np.full(N_total, U_val))\n",
+    "    e, _ = solve_fci(\n",
+    "        h.generate_one_body_integral(dense=True, basis='spatial basis'),\n",
+    "        h.generate_two_body_integral(dense=True, basis='spatial basis', sym=4),\n",
+    "        N_total, nelec, ecore=h.generate_zero_body_integral()\n",
+    "    )\n",
+    "    energies.append(e)\n",
+    "\n",
+    "energies = np.array(energies)"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 27,
+   "metadata": {},
+   "outputs": [
+    {
+     "data": {
+      "image/png": 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",
+      "text/plain": [
+       "<Figure size 960x720 with 1 Axes>"
+      ]
+     },
+     "metadata": {},
+     "output_type": "display_data"
+    }
+   ],
+   "source": [
+    "plt.figure(dpi=150)\n",
+    "plt.plot(v_values, energies, 'o-', linewidth=2, markersize=6)\n",
+    "plt.xlabel(r'Coupling Strength $v_{\\rm ratio} = v/|t|$', fontsize=12)\n",
+    "plt.ylabel(r'Ground State Energy $E_0$', fontsize=12)\n",
+    "plt.title(rf'Picket-Fence Model ($N_{{bus}}={N_bus}$, $U={U_val}$, half-filling)', fontsize=13)\n",
+    "plt.grid(True, linestyle='--', alpha=0.4)\n",
+    "plt.tight_layout()\n",
+    "plt.show()"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "## Physical Interpretation\n",
+    "\n",
+    "- **For small coupling ($v_{\\text{ratio}} \\ll 1$):** Pickets behave as weak perturbations. The energy is dominated by the delocalized bus chain.\n",
+    "- **For large coupling ($v_{\\text{ratio}} \\gg 1$):** The system forms strongly hybridized dimers between each bus site and its picket. The energy decreases significantly as electrons localize on these strong bonds.\n",
+    "\n",
+    "This crossover reflects a transition from a **delocalized 1D metallic-like chain** to a **localized collection of dimers**."
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "## Scaling Considerations\n",
+    "\n",
+    "### Hilbert Space Growth\n",
+    "\n",
+    "At half-filling ($N$ electrons on $2N$ spin-orbitals), the FCI Hilbert space dimension is:\n",
+    "\n",
+    "$$\n",
+    "\\dim(\\mathcal{H}) = \\binom{2N}{N}\n",
+    "$$\n",
+    "\n",
+    "| Sites $N$ | Hilbert space dim | Memory (float64) |\n",
+    "|---|---|---|\n",
+    "| 4 | 70 | ~40 KB |\n",
+    "| 6 | 924 | ~7 MB |\n",
+    "| 8 | 12870 | ~1.3 GB |\n",
+    "| 10 | 184756 | ~270 GB |\n",
+    "\n",
+    "### The Exponential Wall\n",
+    "\n",
+    "FCI scales **exponentially** with system size — both in memory ($O(\\dim^2)$ for the Hamiltonian matrix) and runtime ($O(\\dim^3)$ for diagonalization). Beyond $N \\approx 6$–7 sites per spin, FCI is computationally intractable.\n",
+    "\n",
+    "For larger picket-fence systems, alternative methods include:\n",
+    "- **DMRG** (Density Matrix Renormalization Group) — exploits 1D entanglement structure\n",
+    "- **Tensor Networks** — generalizes to 2D geometries\n",
+    "- **Mean-Field / Hartree-Fock** — upper bound, fast but misses correlations"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "## Extensions\n",
+    "\n",
+    "This framework can be extended to:\n",
+    "- **Disordered picket-fence:** Random on-site energies $\\epsilon_i$ to study Anderson localization.\n",
+    "- **Multi-picket systems:** More than one side-group per bus site.\n",
+    "- **Long-range coupling:** Interactions beyond bus-bus and bus-picket pairs.\n",
+    "- **Time-dependent Hamiltonians:** External fields driving transport through the bus."
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "## 11. Data Persistence\n",
+    "\n",
+    "The Model Hamiltonian package supports saving integrals in two formats:\n",
+    "\n",
+    "1. **`.npz`** — NumPy compressed archive (keys: `e0`, `h1`, `h2`)\n",
+    "2. **`.fcidump`** — Standard quantum chemistry FCIDUMP format\n",
+    "\n",
+    "### 11.1 Saving to `.npz`"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 28,
+   "metadata": {},
+   "outputs": [
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "Saved to picket_fence_integrals.npz\n",
+      "\n",
+      "Keys in .npz file: ['e0', 'h1', 'h2']\n",
+      "  e0 shape: scalar = 0\n",
+      "  h1 shape: (16, 16)\n",
+      "  h2 shape: (16, 16, 16, 16)\n"
+     ]
+    }
+   ],
+   "source": [
+    "# Save to npz\n",
+    "ham_hub.savez('picket_fence_integrals.npz')\n",
+    "print(\"Saved to picket_fence_integrals.npz\")\n",
+    "\n",
+    "# Verify the saved data\n",
+    "data = np.load('picket_fence_integrals.npz')\n",
+    "print(f\"\\nKeys in .npz file: {list(data.keys())}\")\n",
+    "print(f\"  e0 shape: scalar = {data['e0']}\")\n",
+    "print(f\"  h1 shape: {data['h1'].shape}\")\n",
+    "print(f\"  h2 shape: {data['h2'].shape}\")"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "### 11.2 Saving to FCIDUMP format"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 29,
+   "metadata": {},
+   "outputs": [
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "Saved to picket_fence.fcidump\n",
+      "\n",
+      "First 15 lines of picket_fence.fcidump:\n",
+      "   &FCI NORB=16,NELEC=8,MS2=0,\n",
+      "    ORBSYM= 1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,\n",
+      "    ISYM=1\n",
+      "   &END\n",
+      "   2.0000000000000000e+00    9    9    1    1\n",
+      "   2.0000000000000000e+00   10   10    2    2\n",
+      "   2.0000000000000000e+00   11   11    3    3\n",
+      "   2.0000000000000000e+00   12   12    4    4\n",
+      "   2.0000000000000000e+00   13   13    5    5\n",
+      "   2.0000000000000000e+00   14   14    6    6\n",
+      "   2.0000000000000000e+00   15   15    7    7\n",
+      "   2.0000000000000000e+00   16   16    8    8\n",
+      "  -1.0000000000000000e+00    2    1    0    0\n",
+      "  -1.0000000000000000e+00    3    2    0    0\n",
+      "  -1.0000000000000000e+00    4    3    0    0\n",
+      "  ...\n"
+     ]
+    }
+   ],
+   "source": [
+    "# Save to FCIDUMP\n",
+    "ham_hub.save_fcidump('picket_fence.fcidump', nelec=N_elec)\n",
+    "print(\"Saved to picket_fence.fcidump\")\n",
+    "\n",
+    "# Show the first few lines of the FCIDUMP file\n",
+    "print(\"\\nFirst 15 lines of picket_fence.fcidump:\")\n",
+    "with open('picket_fence.fcidump', 'r') as f:\n",
+    "    for i, line in enumerate(f):\n",
+    "        if i < 15:\n",
+    "            print(f\"  {line.rstrip()}\")\n",
+    "        else:\n",
+    "            print(\"  ...\")\n",
+    "            break"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "## Summary & Conclusion\n",
+    "\n",
+    "In this tutorial, we demonstrated the full workflow for modeling a structured system:\n",
+    "\n",
+    "1. **Graph-Based Definition**: Encoding the picket-fence topology via a connectivity matrix in `HamHub`.\n",
+    "2. **Integral Generation**: Extracting 0, 1, and 2-electron integrals in spatial and spin-orbital bases.\n",
+    "3. **Exact Solver**: Computing the ground state using PySCF's FCI (`fci.direct_spin1`).\n",
+    "4. **Pedagogical Verification**: \n",
+    "   - Structural checks of the $h_{pq}$ matrix.\n",
+    "   - Consistency between spin-orbital and geminal energy representations.\n",
+    "   - Validation of limiting cases (isolated bus chain vs. isolated dimers).\n",
+    "5. **Physical Physics Insight**: \n",
+    "   - Quantifying the **localization crossover** using the Inverse Participation Ratio (IPR).\n",
+    "   - Visualizing the transition from a delocalized energy regime to a localized dimer regime.\n",
+    "\n",
+    "### Research Significance\n",
+    "The Picket-Fence model serves as a minimalist archetype for **quasi-1D systems with pendant groups**. By varying the coupling $v_{\\rm ratio}$, one can simulate the transition between a conducting state (high delocalization) and an insulating state (strong localization). This tutorial provides the computational foundation for exploring such transitions in more complex model Hamiltonians."
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "metadata": {},
+   "outputs": [],
+   "source": []
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "metadata": {},
+   "outputs": [],
+   "source": []
+  }
+ ],
+ "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",
+   "version": "3.14.0"
+  }
+ },
+ "nbformat": 4,
+ "nbformat_minor": 4
+}
diff --git a/examples/picket_fence.fcidump b/examples/picket_fence.fcidump
new file mode 100644
index 0000000..8dcfac3
--- /dev/null
+++ b/examples/picket_fence.fcidump
@@ -0,0 +1,27 @@
+ &FCI NORB=16,NELEC=8,MS2=0,
+  ORBSYM= 1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,
+  ISYM=1
+ &END
+ 2.0000000000000000e+00    9    9    1    1
+ 2.0000000000000000e+00   10   10    2    2
+ 2.0000000000000000e+00   11   11    3    3
+ 2.0000000000000000e+00   12   12    4    4
+ 2.0000000000000000e+00   13   13    5    5
+ 2.0000000000000000e+00   14   14    6    6
+ 2.0000000000000000e+00   15   15    7    7
+ 2.0000000000000000e+00   16   16    8    8
+-1.0000000000000000e+00    2    1    0    0
+-1.0000000000000000e+00    3    2    0    0
+-1.0000000000000000e+00    4    3    0    0
+-5.0000000000000000e-01    5    1    0    0
+-5.0000000000000000e-01    6    2    0    0
+-5.0000000000000000e-01    7    3    0    0
+-5.0000000000000000e-01    8    4    0    0
+-1.0000000000000000e+00   10    9    0    0
+-1.0000000000000000e+00   11   10    0    0
+-1.0000000000000000e+00   12   11    0    0
+-5.0000000000000000e-01   13    9    0    0
+-5.0000000000000000e-01   14   10    0    0
+-5.0000000000000000e-01   15   11    0    0
+-5.0000000000000000e-01   16   12    0    0
+ 0.0000000000000000e+00    0    0    0    0
diff --git a/examples/picket_fence_integrals.npz b/examples/picket_fence_integrals.npz
new file mode 100644
index 0000000..bd94fdb
Binary files /dev/null and b/examples/picket_fence_integrals.npz differ