From 0a9e7282dc1aa5b69e095f99f2d82d346b2aabbf Mon Sep 17 00:00:00 2001
From: antoniolrm <am@antoniomanesco.org>
Date: Mon, 23 Oct 2023 15:10:52 +0200
Subject: [PATCH] update examples

---
 examples/1d_hubbard.ipynb                | 301 +++++++++++++++++++++++
 examples/data/1d_hubbard_example.nc      | Bin 0 -> 16980 bytes
 examples/graphene_extended_hubbard.ipynb | 249 ++++++-------------
 3 files changed, 377 insertions(+), 173 deletions(-)
 create mode 100644 examples/1d_hubbard.ipynb
 create mode 100644 examples/data/1d_hubbard_example.nc

diff --git a/examples/1d_hubbard.ipynb b/examples/1d_hubbard.ipynb
new file mode 100644
index 0000000..f4fe2ee
--- /dev/null
+++ b/examples/1d_hubbard.ipynb
@@ -0,0 +1,301 @@
+{
+ "cells": [
+  {
+   "cell_type": "code",
+   "execution_count": 1,
+   "id": "cb509096-42c6-4a45-8dc4-a8eed3116e67",
+   "metadata": {
+    "tags": []
+   },
+   "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 tqdm import tqdm"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 2,
+   "id": "c22c6258-9ee8-4ccf-bfd8-94d50d27114d",
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "def hamiltonian(k):\n",
+    "    tk = (1 + np.exp(1j * k)) * np.eye(2)\n",
+    "    return np.block([\n",
+    "        [0 * np.eye(2), tk],\n",
+    "        [tk.conj(), 0 * np.eye(2)]\n",
+    "    ])"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 3,
+   "id": "d31cbfea-18ea-454e-8a63-d706a85cd3fc",
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "# Compute non-interacting Hamiltonian on a coarse k-point grid\n",
+    "# Number of k-points along each direction\n",
+    "nk = 50\n",
+    "# k-points must start at zero\n",
+    "ks = np.linspace(0, 2 * np.pi, nk, endpoint=False)\n",
+    "hamiltonians_0 = np.array([hamiltonian(k) for k in ks])\n",
+    "hopping_vecs = np.array([[0,], [1,], [-1,]])"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 4,
+   "id": "b39a2976-7c35-4670-83ef-12157bd3fc0e",
+   "metadata": {},
+   "outputs": [
+    {
+     "data": {
+      "image/png": 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",
+      "text/plain": [
+       "<Figure size 640x480 with 1 Axes>"
+      ]
+     },
+     "metadata": {},
+     "output_type": "display_data"
+    }
+   ],
+   "source": [
+    "vals, vecs = np.linalg.eigh(hamiltonians_0)\n",
+    "plt.plot(ks, vals)\n",
+    "plt.show()"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 8,
+   "id": "41bd9f60-8f29-4e7c-a0c4-a0bbf66445b2",
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "def compute_gap(\n",
+    "    H_int,\n",
+    "    ks,\n",
+    "    ks_dense,\n",
+    "    hamiltonians_0=hamiltonians_0,\n",
+    "    filling=2,\n",
+    "    tol=1e-5,\n",
+    "    mixing=0.01,\n",
+    "    order=10,\n",
+    "    guess=None\n",
+    "):\n",
+    "    # Generate guess on the same grid\n",
+    "    if guess is None:\n",
+    "        guess = utils.generate_guess(ks, hopping_vecs, ndof=hamiltonians_0.shape[-1], scale=1)\n",
+    "    else:\n",
+    "        guess += np.max(guess) * utils.generate_guess(ks, hopping_vecs, ndof=hamiltonians_0.shape[-1], scale=0.1)\n",
+    "\n",
+    "    # Find groundstate Hamiltonian on the same grid\n",
+    "    hk = hf.find_groundstate_ham(\n",
+    "        H_int=H_int,\n",
+    "        filling=filling,\n",
+    "        hamiltonians_0=hamiltonians_0,\n",
+    "        tol=tol,\n",
+    "        guess=guess,\n",
+    "        mixing=mixing,\n",
+    "        order=order,\n",
+    "    )\n",
+    "    # Diagonalize groundstate Hamiltonian\n",
+    "    vals, vecs = np.linalg.eigh(hk)\n",
+    "    # Extract dense-grid Fermi energy\n",
+    "    E_F = utils.get_fermi_energy(vals, filling)\n",
+    "    gap = utils.calc_gap(vals, E_F)\n",
+    "    return gap, hk - hamiltonians_0, vals - E_F"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 23,
+   "id": "32b9e7c5-db12-44f9-930c-21e5494404b8",
+   "metadata": {
+    "tags": []
+   },
+   "outputs": [],
+   "source": [
+    "def compute_phase_diagram(\n",
+    "    Us,\n",
+    "    ks,\n",
+    "    ks_dense,\n",
+    "    tol=1e-5,\n",
+    "    mixing=0.01,\n",
+    "    order=10,\n",
+    "):\n",
+    "    # onsite interactions\n",
+    "    v_int = np.block(\n",
+    "        [[np.ones((2, 2)), np.zeros((2, 2))], [np.zeros((2, 2)), np.ones((2, 2))]]\n",
+    "    )\n",
+    "    v_int = np.array([v_int for k in ks])\n",
+    "    gap = []\n",
+    "    vals = []\n",
+    "    guess = None\n",
+    "    for U in tqdm(Us):\n",
+    "        H_int = U * v_int\n",
+    "        _gap, guess, _vals = compute_gap(\n",
+    "            H_int=H_int,\n",
+    "            ks=ks,\n",
+    "            ks_dense=ks_dense,\n",
+    "            tol=tol,\n",
+    "            mixing=mixing,\n",
+    "            order=order,\n",
+    "            guess=guess,\n",
+    "        )\n",
+    "        gap.append(_gap)\n",
+    "        vals.append(_vals)\n",
+    "    return np.asarray(gap, dtype=float), np.asarray(vals)"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 24,
+   "id": "6a8c08a9-7e31-420b-b6b4-709abfb26793",
+   "metadata": {
+    "tags": []
+   },
+   "outputs": [
+    {
+     "name": "stderr",
+     "output_type": "stream",
+     "text": [
+      "100%|██████████| 10/10 [00:07<00:00,  1.34it/s]\n"
+     ]
+    }
+   ],
+   "source": [
+    "# Generate dense-grid k-points\n",
+    "nk_dense = 100\n",
+    "ks_dense = np.linspace(0, 2 * np.pi, nk_dense, endpoint=True)\n",
+    "# Interaction strengths\n",
+    "Us = np.linspace(0, 3, 10, endpoint=True)\n",
+    "gap, vals = compute_phase_diagram(Us, ks=ks, ks_dense=ks_dense, tol=1e-9)"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 25,
+   "id": "e17fc96c-c463-4e1f-8250-c254d761b92a",
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "import xarray as xr\n",
+    "\n",
+    "ds = xr.Dataset(\n",
+    "    data_vars=dict(\n",
+    "        vals=([\"Us\", \"ks\", \"n\"], vals),\n",
+    "        gap=([\"Us\"], gap)\n",
+    "    ),\n",
+    "    coords=dict(Us=Us, ks=ks, n=np.arange(vals.shape[-1])),\n",
+    ")"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 26,
+   "id": "868cf368-45a0-465e-b042-6182ff8b6998",
+   "metadata": {},
+   "outputs": [
+    {
+     "data": {
+      "text/plain": [
+       "<matplotlib.lines.Line2D at 0x7f008b4ef350>"
+      ]
+     },
+     "execution_count": 26,
+     "metadata": {},
+     "output_type": "execute_result"
+    },
+    {
+     "data": {
+      "image/png": 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",
+      "text/plain": [
+       "<Figure size 640x480 with 2 Axes>"
+      ]
+     },
+     "metadata": {},
+     "output_type": "display_data"
+    }
+   ],
+   "source": [
+    "ds.vals.plot.scatter(x='ks', hue='Us')\n",
+    "plt.axhline(0)"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 27,
+   "id": "ac2eb725-f3bd-4d5b-a509-85d0d0071958",
+   "metadata": {},
+   "outputs": [
+    {
+     "data": {
+      "text/plain": [
+       "[<matplotlib.lines.Line2D at 0x7f007257b690>]"
+      ]
+     },
+     "execution_count": 27,
+     "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": [
+    "ds.gap.plot()"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 28,
+   "id": "0cb395cd-84d1-49b4-89dd-da7a2d09c8d0",
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "ds.to_netcdf('./data/1d_hubbard_example.nc')"
+   ]
+  }
+ ],
+ "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": "3.11.5"
+  },
+  "widgets": {
+   "application/vnd.jupyter.widget-state+json": {
+    "state": {},
+    "version_major": 2,
+    "version_minor": 0
+   }
+  }
+ },
+ "nbformat": 4,
+ "nbformat_minor": 5
+}
diff --git a/examples/data/1d_hubbard_example.nc b/examples/data/1d_hubbard_example.nc
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HcmV?d00001

diff --git a/examples/graphene_extended_hubbard.ipynb b/examples/graphene_extended_hubbard.ipynb
index 6d1743b..1133c3b 100644
--- a/examples/graphene_extended_hubbard.ipynb
+++ b/examples/graphene_extended_hubbard.ipynb
@@ -12,67 +12,31 @@
     "import kwant\n",
     "import numpy as np\n",
     "import matplotlib.pyplot as plt\n",
-    "from codes import utils, hf\n",
-    "from scipy.optimize import anderson\n",
-    "from tqdm import tqdm\n",
-    "\n",
-    "s0 = np.identity(2)\n",
-    "sz = np.diag([1, -1])\n",
-    "\n",
-    "norbs=2\n",
-    "\n",
-    "graphene = kwant.lattice.general(\n",
-    "    [[1, 0], [1 / 2, np.sqrt(3) / 2]], [[0, 0], [0, 1 / np.sqrt(3)]],\n",
-    "    norbs=norbs\n",
-    ")\n",
-    "a, b = graphene.sublattices\n",
-    "\n",
-    "# create bulk system\n",
-    "bulk_graphene = kwant.Builder(kwant.TranslationalSymmetry(*graphene.prim_vecs))\n",
-    "# add sublattice potential\n",
-    "m0 = 0\n",
-    "bulk_graphene[a.shape((lambda pos: True), (0, 0))] = m0 * sz\n",
-    "bulk_graphene[b.shape((lambda pos: True), (0, 0))] = -m0 * sz\n",
-    "# add hoppings between sublattices\n",
-    "bulk_graphene[graphene.neighbors(1)] = s0\n",
-    "\n",
-    "# use kwant wraparound to sample bulk k-space\n",
-    "wrapped_syst = kwant.wraparound.wraparound(bulk_graphene)\n",
-    "wrapped_fsyst = kwant.wraparound.wraparound(bulk_graphene).finalized()"
+    "from codes import utils, hf, kwant_examples\n",
+    "from tqdm import tqdm"
    ]
   },
   {
    "cell_type": "code",
    "execution_count": 2,
-   "id": "9cc3b32d-404f-4bc5-a338-83571c9e4c4b",
-   "metadata": {
-    "tags": []
-   },
+   "id": "9ebc3cce-0338-4616-8021-9fecee76f178",
+   "metadata": {},
    "outputs": [],
    "source": [
-    "def func_onsite(site, U):\n",
-    "    return U * np.ones((2, 2))\n",
-    "\n",
-    "def func_hop(site1, site2, V):\n",
-    "    rij = np.linalg.norm(site1.pos - site2.pos)\n",
-    "    return V * np.ones((2, 2))\n",
-    "\n",
-    "def calculate_Hint(U, V, Uk, Vk):\n",
-    "    return U * Uk + V * Vk"
+    "# Create translationally-invariant `kwant.Builder`\n",
+    "bulk_graphene, syst_V = kwant_examples.graphene_extended_hubbard()"
    ]
   },
   {
    "cell_type": "code",
    "execution_count": 3,
-   "id": "a341e0e5-330e-48d1-a20f-a0040688a9d7",
+   "id": "c2dd6c3c-d9bb-4833-b1a0-d28c5d5a935c",
    "metadata": {},
    "outputs": [],
    "source": [
-    "nk = 10\n",
-    "# Generate coarse-grid k-points\n",
-    "ks, dk = np.linspace(0, 2 * np.pi, nk, endpoint=False, retstep=True)\n",
-    "# Generate Hamiltonian on a k-point grid\n",
-    "hamiltonians_0 = utils.syst2hamiltonian(ks=ks, syst=wrapped_fsyst)"
+    "# Extract hopping vectors from dummy interacting system\n",
+    "hopping_vecs = utils.extract_hopping_vectors(syst_V)\n",
+    "hopping_vecs = np.unique(np.stack([*hopping_vecs, *-hopping_vecs]), axis=(0))"
    ]
   },
   {
@@ -84,50 +48,50 @@
    },
    "outputs": [],
    "source": [
-    "Us = np.linspace(0, 4, 50)\n",
-    "Vs = np.linspace(0, 1.5, 20)"
+    "# Use wraparound to make infinite system\n",
+    "wrapped_syst = kwant.wraparound.wraparound(bulk_graphene).finalized()\n",
+    "wrapped_V = kwant.wraparound.wraparound(syst_V).finalized()"
    ]
   },
   {
    "cell_type": "code",
    "execution_count": 5,
-   "id": "32b9e7c5-db12-44f9-930c-21e5494404b8",
-   "metadata": {
-    "tags": []
-   },
+   "id": "d31cbfea-18ea-454e-8a63-d706a85cd3fc",
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "# Compute non-interacting Hamiltonian on a coarse k-point grid\n",
+    "# Number of k-points along each direction\n",
+    "nk = 15\n",
+    "# k-points must start at zero\n",
+    "ks = np.linspace(0, 2 * np.pi, nk, endpoint=False)\n",
+    "hamiltonians_0 = utils.syst2hamiltonian(ks, wrapped_syst)"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 6,
+   "id": "41bd9f60-8f29-4e7c-a0c4-a0bbf66445b2",
+   "metadata": {},
    "outputs": [],
    "source": [
-    "_, deltas = utils.generate_scf_syst(\n",
-    "    max_neighbor=1, syst=wrapped_syst, lattice=graphene\n",
-    ")\n",
-    "deltas = np.asarray(deltas) #deltas are the hopping vecs\n",
-    "deltas = np.unique(np.stack([*deltas, *-deltas]), axis=(0))\n",
-    "\n",
     "def compute_gap(\n",
-    "    U,\n",
-    "    V,\n",
     "    H_int,\n",
-    "    max_neighbor=1,\n",
-    "    lattice=graphene,\n",
+    "    ks,\n",
+    "    ks_dense,\n",
+    "    hamiltonians_0=hamiltonians_0,\n",
     "    filling=2,\n",
-    "    nk=12,\n",
     "    tol=1e-5,\n",
-    "    norbs=norbs,\n",
-    "    nk_dense=30,\n",
-    "    mixing=0.5,\n",
-    "    order=1,\n",
+    "    mixing=0.01,\n",
+    "    order=10,\n",
     "    guess=None\n",
     "):\n",
-    "    # Generate coarse-grid k-points\n",
-    "    ks, dk = np.linspace(0, 2 * np.pi, nk, endpoint=False, retstep=True)\n",
-    "    # Generate Hamiltonian on a k-point grid\n",
-    "    hamiltonians_0 = utils.syst2hamiltonian(ks=ks, syst=wrapped_fsyst)\n",
     "    # Generate guess on the same grid\n",
     "    if guess is None:\n",
-    "        guess = utils.generate_guess(ks, deltas, ndof=hamiltonians_0.shape[-1], scale=1)\n",
+    "        guess = utils.generate_guess(ks, hopping_vecs, ndof=hamiltonians_0.shape[-1], scale=1)\n",
     "    else:\n",
-    "        guess += np.max(guess) * utils.generate_guess(ks, deltas, ndof=hamiltonians_0.shape[-1], scale=0.1)\n",
-    "    \n",
+    "        guess += np.max(guess) * utils.generate_guess(ks, hopping_vecs, ndof=hamiltonians_0.shape[-1], scale=0.1)\n",
+    "\n",
     "    # Find groundstate Hamiltonian on the same grid\n",
     "    hk = hf.find_groundstate_ham(\n",
     "        H_int=H_int,\n",
@@ -138,55 +102,42 @@
     "        mixing=mixing,\n",
     "        order=order,\n",
     "    )\n",
-    "    # Diagonalize groundstate Hamiltonian\n",
-    "    vals, vecs = np.linalg.eigh(hk)\n",
-    "    # Extract coarse-grid Fermi energy\n",
-    "    E_F = utils.get_fermi_energy(vals, 2)\n",
-    "    # Generate dense-grid k-points\n",
-    "    ks_dense = np.linspace(0, 2 * np.pi, nk_dense, endpoint=False)\n",
     "    # Compute groundstate Hamiltonian on a dense grid\n",
-    "    scf_ham = utils.hk_densegrid(hk, ks, ks_dense, deltas)\n",
+    "    scf_ham = utils.hk_densegrid(hk, ks, ks_dense, hopping_vecs)\n",
     "    # Diagonalize groundstate Hamiltonian\n",
     "    vals, vecs = np.linalg.eigh(scf_ham)\n",
     "    # Extract dense-grid Fermi energy\n",
-    "    E_F = utils.get_fermi_energy(vals, 2)\n",
-    "\n",
+    "    E_F = utils.get_fermi_energy(vals, filling)\n",
     "    gap = utils.calc_gap(vals, E_F)\n",
-    "    return gap, hk\n",
-    "\n",
-    "\n",
-    "def compute_phase_diagram(Us, Vs, nk, tol, mixing, order):\n",
-    "    import qsymm\n",
-    "    import adaptive\n",
-    "    from codes import utils, hf\n",
-    "\n",
-    "    ks = np.linspace(0, 2 * np.pi, nk, endpoint=False)\n",
-    "\n",
-    "    Uk = utils.potential2hamiltonian(\n",
-    "        syst=wrapped_syst,\n",
-    "        lattice=graphene,\n",
-    "        func_onsite=func_onsite,\n",
-    "        func_hop=func_hop,\n",
-    "        params=dict(U=1, V=0),\n",
-    "        ks=ks,\n",
-    "    )\n",
-    "\n",
-    "    Vk = utils.potential2hamiltonian(\n",
-    "        syst=wrapped_syst,\n",
-    "        lattice=graphene,\n",
-    "        func_onsite=func_onsite,\n",
-    "        func_hop=func_hop,\n",
-    "        params=dict(U=0, V=1),\n",
-    "        ks=ks,\n",
-    "    )\n",
+    "    return gap, hk - hamiltonians_0"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 7,
+   "id": "32b9e7c5-db12-44f9-930c-21e5494404b8",
+   "metadata": {
+    "tags": []
+   },
+   "outputs": [],
+   "source": [
+    "def compute_phase_diagram(Us, Vs, ks, ks_dense, tol, mixing, order):\n",
+    "    Uk = utils.syst2hamiltonian(ks, wrapped_V, params=dict(U=1, V=0))\n",
+    "    Vk = utils.syst2hamiltonian(ks, wrapped_V, params=dict(U=0, V=1))\n",
     "    gap = []\n",
     "    for U in tqdm(Us):\n",
     "        guess = None\n",
     "        gap_U = []\n",
     "        for V in Vs:\n",
-    "            H_int = calculate_Hint(U, V, Uk, Vk)\n",
+    "            H_int = U * Uk + V * Vk\n",
     "            _gap, guess = compute_gap(\n",
-    "                U=U, V=V, H_int=H_int, nk=nk, tol=tol, mixing=mixing, order=order, guess=guess\n",
+    "                H_int=H_int,\n",
+    "                ks=ks,\n",
+    "                ks_dense=ks_dense,\n",
+    "                tol=tol,\n",
+    "                mixing=mixing,\n",
+    "                order=order,\n",
+    "                guess=guess,\n",
     "            )\n",
     "            gap_U.append(_gap)\n",
     "        gap.append(gap_U)\n",
@@ -195,7 +146,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 14,
+   "execution_count": null,
    "id": "6a8c08a9-7e31-420b-b6b4-709abfb26793",
    "metadata": {
     "tags": []
@@ -205,55 +156,39 @@
      "name": "stderr",
      "output_type": "stream",
      "text": [
-      "  8%|â–Š         | 4/50 [03:05<34:05, 44.48s/it]/opt/conda/lib/python3.11/site-packages/scipy/optimize/_nonlin.py:1074: LinAlgWarning: Ill-conditioned matrix (rcond=1.67985e-18): result may not be accurate.\n",
-      "  gamma = solve(self.a, df_f)\n",
-      "/opt/conda/lib/python3.11/site-packages/scipy/optimize/_nonlin.py:1074: LinAlgWarning: Ill-conditioned matrix (rcond=1.35418e-18): result may not be accurate.\n",
-      "  gamma = solve(self.a, df_f)\n",
-      "/opt/conda/lib/python3.11/site-packages/scipy/optimize/_nonlin.py:1074: LinAlgWarning: Ill-conditioned matrix (rcond=1.65467e-17): result may not be accurate.\n",
-      "  gamma = solve(self.a, df_f)\n",
-      "/opt/conda/lib/python3.11/site-packages/scipy/optimize/_nonlin.py:1074: LinAlgWarning: Ill-conditioned matrix (rcond=1.41405e-17): result may not be accurate.\n",
-      "  gamma = solve(self.a, df_f)\n",
-      " 10%|â–ˆ         | 5/50 [03:39<30:38, 40.86s/it]/opt/conda/lib/python3.11/site-packages/scipy/optimize/_nonlin.py:1074: LinAlgWarning: Ill-conditioned matrix (rcond=1.08904e-17): result may not be accurate.\n",
-      "  gamma = solve(self.a, df_f)\n",
-      " 46%|████▌     | 23/50 [18:08<21:08, 46.97s/it]/opt/conda/lib/python3.11/site-packages/scipy/optimize/_nonlin.py:1074: LinAlgWarning: Ill-conditioned matrix (rcond=8.96238e-17): result may not be accurate.\n",
-      "  gamma = solve(self.a, df_f)\n",
-      " 58%|█████▊    | 29/50 [34:18<1:09:00, 197.17s/it]/opt/conda/lib/python3.11/site-packages/scipy/optimize/_nonlin.py:1074: LinAlgWarning: Ill-conditioned matrix (rcond=5.74155e-17): result may not be accurate.\n",
-      "  gamma = solve(self.a, df_f)\n",
-      "/opt/conda/lib/python3.11/site-packages/scipy/optimize/_nonlin.py:1074: LinAlgWarning: Ill-conditioned matrix (rcond=4.45034e-17): result may not be accurate.\n",
-      "  gamma = solve(self.a, df_f)\n",
-      "/opt/conda/lib/python3.11/site-packages/scipy/optimize/_nonlin.py:1074: LinAlgWarning: Ill-conditioned matrix (rcond=1.19451e-18): result may not be accurate.\n",
-      "  gamma = solve(self.a, df_f)\n",
-      "/opt/conda/lib/python3.11/site-packages/scipy/optimize/_nonlin.py:1074: LinAlgWarning: Ill-conditioned matrix (rcond=2.7833e-17): result may not be accurate.\n",
-      "  gamma = solve(self.a, df_f)\n",
-      "/opt/conda/lib/python3.11/site-packages/scipy/optimize/_nonlin.py:1074: LinAlgWarning: Ill-conditioned matrix (rcond=1.16944e-17): result may not be accurate.\n",
-      "  gamma = solve(self.a, df_f)\n",
-      "100%|██████████| 50/50 [1:22:22<00:00, 98.86s/it] \n"
+      "  0%|          | 0/10 [00:00<?, ?it/s]"
      ]
     }
    ],
    "source": [
-    "gap = compute_phase_diagram(Us, Vs, nk=15, tol=1e-5, mixing=0.01, order=10)"
+    "# Generate dense-grid k-points\n",
+    "nk_dense = 30\n",
+    "ks_dense = np.linspace(0, 2 * np.pi, nk_dense, endpoint=False)\n",
+    "# Interaction strengths\n",
+    "Us = np.linspace(0, 4, 10, endpoint=True)\n",
+    "Vs = np.linspace(0, 1.5, 10, endpoint=True)\n",
+    "gap = compute_phase_diagram(Us, Vs, ks=ks, ks_dense=ks_dense, tol=1e-4, mixing=0.01, order=10)"
    ]
   },
   {
    "cell_type": "code",
-   "execution_count": 15,
+   "execution_count": 11,
    "id": "39edbf19",
    "metadata": {},
    "outputs": [
     {
      "data": {
       "text/plain": [
-       "<matplotlib.colorbar.Colorbar at 0x7fee6ee82690>"
+       "<matplotlib.colorbar.Colorbar at 0x7f0a0d7c18d0>"
       ]
      },
-     "execution_count": 15,
+     "execution_count": 11,
      "metadata": {},
      "output_type": "execute_result"
     },
     {
      "data": {
-      "image/png": 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",
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",
       "text/plain": [
        "<Figure size 640x480 with 2 Axes>"
       ]
@@ -267,38 +202,6 @@
     "plt.colorbar()"
    ]
   },
-  {
-   "cell_type": "code",
-   "execution_count": 16,
-   "id": "27f9d0d8",
-   "metadata": {},
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "<matplotlib.colorbar.Colorbar at 0x7fee6ed3e910>"
-      ]
-     },
-     "execution_count": 16,
-     "metadata": {},
-     "output_type": "execute_result"
-    },
-    {
-     "data": {
-      "image/png": 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",
-      "text/plain": [
-       "<Figure size 640x480 with 2 Axes>"
-      ]
-     },
-     "metadata": {},
-     "output_type": "display_data"
-    }
-   ],
-   "source": [
-    "plt.imshow((gap).T, origin='lower', extent=(Us.min(), Us.max(), Vs.min(), Vs.max()), vmin=0)\n",
-    "plt.colorbar()"
-   ]
-  },
   {
    "cell_type": "code",
    "execution_count": 17,
-- 
GitLab