From 4ed37a6865debdfbe05a7134358efe3a4f3f7d41 Mon Sep 17 00:00:00 2001
From: Kostas Vilkelis <kostasvilkelis@gmail.com>
Date: Tue, 30 Jan 2024 13:27:27 +0100
Subject: [PATCH] push total energy check

---
 examples/tEnergyTest.ipynb | 155 +++++++++++++++++++++++++++++++++++++
 1 file changed, 155 insertions(+)
 create mode 100644 examples/tEnergyTest.ipynb

diff --git a/examples/tEnergyTest.ipynb b/examples/tEnergyTest.ipynb
new file mode 100644
index 0000000..dad50e2
--- /dev/null
+++ b/examples/tEnergyTest.ipynb
@@ -0,0 +1,155 @@
+{
+ "cells": [
+  {
+   "cell_type": "code",
+   "execution_count": 1,
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "import numpy as np\n",
+    "import matplotlib.pyplot as plt\n",
+    "from codes import utils, model, interface, solvers, hf"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 2,
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "hopp = np.kron(np.array([[0, 1], [0, 0]]), np.eye(2))\n",
+    "tb_model = {(0,): hopp + hopp.T.conj(), (1,): hopp, (-1,): hopp.T.conj()}\n",
+    "\n",
+    "\n",
+    "# define interaction\n",
+    "def intModel(U):\n",
+    "    model = {\n",
+    "        (0,): U * np.kron(np.ones((2, 2)), np.eye(2)),\n",
+    "    }\n",
+    "    return model"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 6,
+   "metadata": {},
+   "outputs": [
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "-2.2252238082028337\n"
+     ]
+    }
+   ],
+   "source": [
+    "U0 = 1\n",
+    "nk = 100\n",
+    "filling = 2\n",
+    "\n",
+    "hamiltonians_0 = utils.kgrid_hamiltonian(\n",
+    "    nk=nk, hk=utils.model2hk(tb_model=tb_model), dim=1\n",
+    ")\n",
+    "\n",
+    "def groundstate(U):\n",
+    "    tb_mf = model.Model(tb_model=tb_model, int_model=intModel(U))\n",
+    "    tb_mf_k = interface.find_groundstate_ham(\n",
+    "        tb_mf,\n",
+    "        filling=filling,\n",
+    "        nk=nk,\n",
+    "        solver=solvers.rspace_solver,\n",
+    "        cost_function=solvers.real_space_cost,\n",
+    "        return_kspace=True,\n",
+    "    )\n",
+    "    vals, vecs = np.linalg.eigh(tb_mf_k)\n",
+    "    EF = utils.get_fermi_energy(vals, filling)\n",
+    "    densityMatrix = hf.density_matrix(vals, vecs, EF)\n",
+    "\n",
+    "    return tb_mf_k, densityMatrix\n",
+    "\n",
+    "@np.vectorize\n",
+    "def groundstateEnergy(U):\n",
+    "    _, densityMatrix = groundstate(U)\n",
+    "    Vk = utils.model2hk(tb_model=intModel(U))\n",
+    "    H_int = utils.kgrid_hamiltonian(nk=nk, hk=Vk, dim=1)\n",
+    "    mf = hf.compute_mf(densityMatrix, H_int)\n",
+    "    return hf.total_energy(mf + hamiltonians_0, densityMatrix)\n",
+    "\n",
+    "tb_mf0, densityMatrix0 = groundstate(U0)\n",
+    "print(groundstateEnergy(U0))\n",
+    "\n",
+    "@np.vectorize\n",
+    "def otherEnergy(U):\n",
+    "    # Total Energy with density matrix from the groundstate at U0\n",
+    "    Vk = utils.model2hk(tb_model=intModel(U))\n",
+    "    H_int = utils.kgrid_hamiltonian(nk=nk, hk=Vk, dim=1)\n",
+    "    mf = hf.compute_mf(densityMatrix0, H_int)\n",
+    "    return hf.total_energy(mf + hamiltonians_0, densityMatrix0)"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 9,
+   "metadata": {},
+   "outputs": [
+    {
+     "data": {
+      "text/plain": [
+       "<matplotlib.legend.Legend at 0x7ff797ad0450>"
+      ]
+     },
+     "execution_count": 9,
+     "metadata": {},
+     "output_type": "execute_result"
+    },
+    {
+     "data": {
+      "image/png": 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",
+      "text/plain": [
+       "<Figure size 640x480 with 1 Axes>"
+      ]
+     },
+     "metadata": {},
+     "output_type": "display_data"
+    }
+   ],
+   "source": [
+    "U_list = np.linspace(U0 - 0.2, U0 + 0.2, 10)\n",
+    "plt.plot(U_list, otherEnergy(U_list), label='MF groundstate from U=1')\n",
+    "plt.plot(U_list, groundstateEnergy(U_list), label='MF groundstate')\n",
+    "plt.axvline(x=1, c='k', ls='--')\n",
+    "plt.ylabel('Total Energy')\n",
+    "plt.xlabel('U')\n",
+    "plt.legend()"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "metadata": {},
+   "outputs": [],
+   "source": []
+  }
+ ],
+ "metadata": {
+  "kernelspec": {
+   "display_name": "base",
+   "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": "3.11.7"
+  }
+ },
+ "nbformat": 4,
+ "nbformat_minor": 2
+}
-- 
GitLab