From 572cf322c820c2977cedd650b8fc030a948ec9d4 Mon Sep 17 00:00:00 2001
From: antoniolrm <am@antoniomanesco.org>
Date: Mon, 23 Oct 2023 17:24:53 +0200
Subject: [PATCH] clean up molecule example and add notes:

---
 examples/data/diatomic_molecule_example.nc | Bin 13468 -> 13468 bytes
 examples/diatomic_molecule.ipynb           | 125 ++++++++++++++-------
 2 files changed, 87 insertions(+), 38 deletions(-)

diff --git a/examples/data/diatomic_molecule_example.nc b/examples/data/diatomic_molecule_example.nc
index 58bf3a250d1905535e8dc0161494465e597fe8ff..b400786ecadaed279b1db5d59b1acb57431880a0 100644
GIT binary patch
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diff --git a/examples/diatomic_molecule.ipynb b/examples/diatomic_molecule.ipynb
index 3b537a2..81f1b95 100644
--- a/examples/diatomic_molecule.ipynb
+++ b/examples/diatomic_molecule.ipynb
@@ -17,51 +17,64 @@
     "from itertools import product"
    ]
   },
+  {
+   "cell_type": "markdown",
+   "id": "2b76e5f0-75f0-4812-9a3a-39992f0244e7",
+   "metadata": {},
+   "source": [
+    "In this example, we will build a zero-dimensional model. Namely, we will find the Hartree-Fock groundstate solution for a diatomic molecule with onsite and nearest-neighbor interactions.\n",
+    "\n",
+    "We start by writing the non-interacting Hamiltonian. The minimal tight-binding model has the following Hamiltonian:\n",
+    "$$\n",
+    " H_0 = c_L^{\\dagger} c_R + h.c.\n",
+    "$$\n",
+    "which we can rewrite in following matrix representation:\n",
+    "$$\n",
+    "H_0 = \\left(c_L^{\\dagger}~c_R^{\\dagger}\\right) \\left(\\begin{array}{cc}\n",
+    "    0 & \\mathbb{1}\\\\\n",
+    "    \\mathbb{1} & 0\n",
+    "\\end{array}\\right)\n",
+    "\\left(\\begin{array}{c}\n",
+    "    c_L\\\\\n",
+    "    c_R\n",
+    "\\end{array}\\right)\n",
+    "$$\n",
+    "where $\\mathbb{1}$ is a $2\\times 2$ identity matrix."
+   ]
+  },
   {
    "cell_type": "code",
-   "execution_count": 2,
+   "execution_count": 86,
    "id": "d31cbfea-18ea-454e-8a63-d706a85cd3fc",
    "metadata": {},
    "outputs": [],
    "source": [
+    "# Just writing the Hamiltonian above in numpy\n",
     "hamiltonian_0 = np.block([\n",
     "    [0 * np.eye(2), np.eye(2)],\n",
     "    [np.eye(2), 0 * np.eye(2)]\n",
     "])\n",
-    "hamiltonian_0 = np.expand_dims(hamiltonian_0, axis=0)\n",
-    "hopping_vecs = np.array([[0,]])"
+    "# Here we add a dummy index because that is interpreted as a Γ-point calculation.\n",
+    "hamiltonian_0 = np.expand_dims(hamiltonian_0, axis=0)"
    ]
   },
   {
-   "cell_type": "code",
-   "execution_count": 3,
-   "id": "46e26a1c-36bd-48bd-89e5-5a7faffa3d1e",
+   "cell_type": "markdown",
+   "id": "4c0d41ff-8231-441f-89a3-35f3fe94c57a",
    "metadata": {},
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "(1, 4, 4)"
-      ]
-     },
-     "execution_count": 3,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
    "source": [
-    "hamiltonian_0.shape"
+    "We can naturally compute the eigenvalues for inspection."
    ]
   },
   {
    "cell_type": "code",
-   "execution_count": 4,
+   "execution_count": 85,
    "id": "b39a2976-7c35-4670-83ef-12157bd3fc0e",
    "metadata": {},
    "outputs": [
     {
      "data": {
-      "image/png": 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",
       "text/plain": [
        "<Figure size 640x480 with 1 Axes>"
       ]
@@ -71,14 +84,25 @@
     }
    ],
    "source": [
-    "vals, vecs = np.linalg.eigh(hamiltonian_0)\n",
+    "vals, vecs = np.linalg.eigh(hamiltonian_0[0])\n",
     "plt.plot(vals, 'o')\n",
     "plt.show()"
    ]
   },
+  {
+   "cell_type": "markdown",
+   "id": "688558ce-cc8e-418e-846e-4e3e32cb3193",
+   "metadata": {},
+   "source": [
+    "We now move to an eigenvalue calculation of the Hartree-Fock solution. The workflow is rather simple:\n",
+    "* Generate a random guess.\n",
+    "* Run the self-consistent loop.\n",
+    "* Diagonalize the mean-field Hamiltonian."
+   ]
+  },
   {
    "cell_type": "code",
-   "execution_count": 57,
+   "execution_count": 91,
    "id": "41bd9f60-8f29-4e7c-a0c4-a0bbf66445b2",
    "metadata": {},
    "outputs": [],
@@ -92,13 +116,10 @@
     "    order=10,\n",
     "    guess=None\n",
     "):\n",
-    "    # Generate guess on the same grid\n",
-    "    if guess is None:\n",
-    "        guess = utils.generate_guess([0], hopping_vecs, ndof=hamiltonian_0.shape[-1], scale=1)\n",
-    "    else:\n",
-    "        guess += np.max(guess) * utils.generate_guess([0], hopping_vecs, ndof=hamiltonian_0.shape[-1], scale=0.1)\n",
+    "    # Generate random guess with same shape as the Hamiltonian.\n",
+    "    guess = np.random.rand(*hamiltonian_0.shape) * np.exp(1j * 2 * np.pi * np.random.rand(*hamiltonian_0.shape))\n",
     "\n",
-    "    # Find groundstate Hamiltonian on the same grid\n",
+    "    # Run SCF loop to find groundstate Hamiltonian.\n",
     "    h = hf.find_groundstate_ham(\n",
     "        H_int=H_int,\n",
     "        filling=filling,\n",
@@ -108,16 +129,44 @@
     "        mixing=mixing,\n",
     "        order=order,\n",
     "    )\n",
-    "    # Diagonalize groundstate Hamiltonian\n",
+    "    # Diagonalize groundstate Hamiltonian.\n",
     "    vals, vecs = np.linalg.eigh(h)\n",
-    "    # Extract dense-grid Fermi energy\n",
+    "    # Extract Fermi energy.\n",
     "    E_F = utils.get_fermi_energy(vals, filling)\n",
     "    return vals - E_F"
    ]
   },
+  {
+   "cell_type": "markdown",
+   "id": "9e580757-adad-4e20-b60c-cff8a85b633d",
+   "metadata": {},
+   "source": [
+    "And then we use this workflow to compute the phase diagram. We consider an interacting Hamiltonian with onsite and nearest-neighbor interactions:\n",
+    "\\begin{align}\n",
+    "H_{int} = \\sum_i U_i n_i n_i + \\sum_{\\langle i, j \\rangle} V_{ij} n_i n_j\\\\\n",
+    "= \\sum_i U_i n_{i\\uparrow} n_{i\\downarrow} + \\sum_{\\langle i, j \\rangle} V_{ij} n_i n_j\n",
+    "\\end{align}\n",
+    "where from the first to the second line we removed the terms that are not allowed by the exclusion principle. These are however taken care of by the algorithm, so we in fact just need to provide $U_i$ and $V_{ij}$. We simplify the Hamiltonian further as:\n",
+    "\\begin{align}\n",
+    "H_{int} = U \\sum_i n_{i\\uparrow} n_{i\\downarrow} + V_{ij} \\sum_{\\langle i, j \\rangle} n_i n_j~.\n",
+    "\\end{align}\n",
+    "Thus, the we just need to pass to the algorithm the matrix\n",
+    "$$\n",
+    "H_{int} =\n",
+    "\\left(\\begin{array}{cccc}\n",
+    "    U & U & V & V\\\\\n",
+    "    U & U & V & V\\\\\n",
+    "    V & V & U & U\\\\\n",
+    "    V & V & U & U\n",
+    "\\end{array}\\right)~.\n",
+    "$$\n",
+    "\n",
+    "We thus sweep these parameters and see how the eigenvalues evolve."
+   ]
+  },
   {
    "cell_type": "code",
-   "execution_count": 79,
+   "execution_count": 99,
    "id": "32b9e7c5-db12-44f9-930c-21e5494404b8",
    "metadata": {
     "tags": []
@@ -160,7 +209,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 81,
+   "execution_count": null,
    "id": "6a8c08a9-7e31-420b-b6b4-709abfb26793",
    "metadata": {
     "tags": []
@@ -170,7 +219,7 @@
      "name": "stderr",
      "output_type": "stream",
      "text": [
-      "100%|██████████| 20/20 [01:02<00:00,  3.15s/it]\n"
+      " 65%|██████▌   | 13/20 [00:34<00:32,  4.62s/it]"
      ]
     }
    ],
@@ -183,7 +232,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 82,
+   "execution_count": 94,
    "id": "e17fc96c-c463-4e1f-8250-c254d761b92a",
    "metadata": {},
    "outputs": [],
@@ -200,13 +249,13 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 83,
+   "execution_count": 95,
    "id": "868cf368-45a0-465e-b042-6182ff8b6998",
    "metadata": {},
    "outputs": [
     {
      "data": {
-      "image/png": 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rQHqQ70BycckYSqbt1pSTJk3SsGHDcuurqqo0b948HXPMMTr11FOVyWR0//33RxgpgO4g14F0INeB9CDfgWTikjEAAAAAAICU4QwhAAAAAACAlKEgBAAAAAAAkDIUhAAAAAAAAFKGghAAAAAAAEDKUBACAAAAAABIGQpCAAAAAAAAKUNBCAAAAAAAIGUoCAEAAAAAAKQMBSEAAAAAAICUoSAEAAAAAACQMhSEAAAAAAAAUoaCEAAAAAAAQMr8f2APv9rkRmJGAAAAAElFTkSuQmCC",
       "text/plain": [
        "<Figure size 1300x300 with 5 Axes>"
       ]
@@ -222,7 +271,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 37,
+   "execution_count": 97,
    "id": "0cb395cd-84d1-49b4-89dd-da7a2d09c8d0",
    "metadata": {},
    "outputs": [],
-- 
GitLab