From 2f7f5b59779406a31c2974c0d80037860bbb3a0c Mon Sep 17 00:00:00 2001
From: Antonio Manesco <am@antoniomanesco.org>
Date: Thu, 9 Nov 2023 10:30:33 +0100
Subject: [PATCH] adapt Hubbard 1D example

---
 examples/1d_hubbard.ipynb           |  72 +++++++++++++++++-----------
 examples/data/1d_hubbard_example.nc | Bin 65540 -> 65540 bytes
 2 files changed, 43 insertions(+), 29 deletions(-)

diff --git a/examples/1d_hubbard.ipynb b/examples/1d_hubbard.ipynb
index 79ef0d6..0fec29d 100644
--- a/examples/1d_hubbard.ipynb
+++ b/examples/1d_hubbard.ipynb
@@ -9,10 +9,9 @@
    },
    "outputs": [],
    "source": [
-    "import kwant\n",
     "import numpy as np\n",
     "import matplotlib.pyplot as plt\n",
-    "from codes import utils, hf, kwant_examples\n",
+    "from codes import utils, hf\n",
     "from tqdm import tqdm"
    ]
   },
@@ -43,6 +42,7 @@
     "tb_model = {\n",
     "    (0,) : hopp + hopp.T.conj(),\n",
     "    (1,) : hopp,\n",
+    "    (-1,) : hopp.T.conj()\n",
     "}"
    ]
   },
@@ -74,8 +74,12 @@
    "source": [
     "# Set number of k-points\n",
     "nk = 100\n",
+    "hk = utils.model2hk(tb_model=tb_model)\n",
     "# Compute Hamiltonian on the corresponding k-point grid\n",
-    "hamiltonians_0, ks = utils.kgrid_hamiltonian(nk, tb_model, return_ks=True)\n",
+    "hamiltonians_0, ks = utils.kgrid_hamiltonian(\n",
+    "    nk=nk, hk=hk, dim=1,\n",
+    "    return_ks=True\n",
+    ")\n",
     "# Perform diagonalization\n",
     "vals, vecs = np.linalg.eigh(hamiltonians_0)\n",
     "# Plot data\n",
@@ -97,34 +101,36 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 33,
+   "execution_count": 4,
    "id": "41bd9f60-8f29-4e7c-a0c4-a0bbf66445b2",
    "metadata": {},
    "outputs": [],
    "source": [
     "def compute_gap(\n",
-    "    tb_model,\n",
-    "    int_model,\n",
+    "    hk,\n",
+    "    Vk,\n",
     "    nk,\n",
     "    nk_dense,\n",
     "    filling=2\n",
     "):\n",
-    "    # Generate guess on the same k-point grid\n",
-    "    guess = utils.generate_guess(nk, tb_model, int_model, scale=1)\n",
-    "\n",
     "    # Find groundstate Hamiltonian on the same grid\n",
-    "    mf_model = hf.find_groundstate_ham(\n",
-    "        int_model=int_model,\n",
+    "    _, mf_model = hf.find_groundstate_ham(\n",
+    "        hk=hk,\n",
+    "        Vk=Vk,\n",
     "        filling=filling,\n",
-    "        tb_model=tb_model,\n",
-    "        guess=guess,\n",
+    "        dim=1,\n",
     "        nk=nk,\n",
-    "        tol=1e-8\n",
+    "        cutoff=1,\n",
+    "        return_model=True\n",
     "    )\n",
     "    # Generate Hamiltonian on a denser k-point grid\n",
-    "    hk = utils.kgrid_hamiltonian(nk_dense, mf_model)\n",
+    "    mf_k = utils.kgrid_hamiltonian(\n",
+    "        nk=nk_dense,\n",
+    "        hk=utils.model2hk(tb_model=mf_model),\n",
+    "        dim=1\n",
+    "    )\n",
     "    # Diagonalize groundstate Hamiltonian\n",
-    "    vals, vecs = np.linalg.eigh(hk)\n",
+    "    vals, _ = np.linalg.eigh(mf_k)\n",
     "    # Extract dense-grid Fermi energy\n",
     "    E_F = utils.get_fermi_energy(vals, filling)\n",
     "    gap = utils.calc_gap(vals, E_F)\n",
@@ -150,7 +156,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 34,
+   "execution_count": 5,
    "id": "32b9e7c5-db12-44f9-930c-21e5494404b8",
    "metadata": {
     "tags": []
@@ -169,9 +175,10 @@
     "        int_model = {\n",
     "            (0,) : U * np.kron(np.ones((2, 2)), np.eye(2))\n",
     "        }\n",
+    "        Vk = utils.model2hk(tb_model=int_model)\n",
     "        _gap, _vals = compute_gap(\n",
-    "            tb_model=tb_model,\n",
-    "            int_model=int_model,\n",
+    "            hk=hk,\n",
+    "            Vk=Vk,\n",
     "            nk=nk,\n",
     "            nk_dense=nk_dense,\n",
     "        )\n",
@@ -182,7 +189,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 126,
+   "execution_count": 6,
    "id": "6a8c08a9-7e31-420b-b6b4-709abfb26793",
    "metadata": {
     "tags": []
@@ -192,7 +199,14 @@
      "name": "stderr",
      "output_type": "stream",
      "text": [
-      "100%|██████████| 20/20 [00:31<00:00,  1.60s/it]\n"
+      "  0%|          | 0/20 [00:00<?, ?it/s]"
+     ]
+    },
+    {
+     "name": "stderr",
+     "output_type": "stream",
+     "text": [
+      "100%|██████████| 20/20 [00:12<00:00,  1.63it/s]\n"
      ]
     }
    ],
@@ -205,7 +219,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 127,
+   "execution_count": 7,
    "id": "e17fc96c-c463-4e1f-8250-c254d761b92a",
    "metadata": {},
    "outputs": [],
@@ -231,7 +245,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 128,
+   "execution_count": 8,
    "id": "868cf368-45a0-465e-b042-6182ff8b6998",
    "metadata": {},
    "outputs": [
@@ -270,7 +284,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 129,
+   "execution_count": 9,
    "id": "ac2eb725-f3bd-4d5b-a509-85d0d0071958",
    "metadata": {},
    "outputs": [
@@ -301,17 +315,17 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 131,
+   "execution_count": 10,
    "id": "5499ea62-cf1b-4a13-8191-ebb73ea38704",
    "metadata": {},
    "outputs": [
     {
      "data": {
       "text/plain": [
-       "array(1.00352528)"
+       "array(1.00352529)"
       ]
      },
-     "execution_count": 131,
+     "execution_count": 10,
      "metadata": {},
      "output_type": "execute_result"
     }
@@ -322,7 +336,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 132,
+   "execution_count": 11,
    "id": "0cb395cd-84d1-49b4-89dd-da7a2d09c8d0",
    "metadata": {},
    "outputs": [],
@@ -347,7 +361,7 @@
    "name": "python",
    "nbconvert_exporter": "python",
    "pygments_lexer": "ipython3",
-   "version": "3.11.5"
+   "version": "3.11.6"
   },
   "widgets": {
    "application/vnd.jupyter.widget-state+json": {
diff --git a/examples/data/1d_hubbard_example.nc b/examples/data/1d_hubbard_example.nc
index 7ea1d4f36266ed22a7b8a12472c15f3f9b41c02b..c973f6b2aaaf2a6d41d0438192854bac87ec2b2b 100644
GIT binary patch
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