From 47572bff07a214a9f7a48455147350acd71d0334 Mon Sep 17 00:00:00 2001
From: antoniolrm <am@antoniomanesco.org>
Date: Fri, 27 Oct 2023 15:23:40 +0200
Subject: [PATCH] update graphene example

---
 examples/data/graphene_example.nc        | Bin 8864 -> 3824 bytes
 examples/graphene_extended_hubbard.ipynb | 106 +++++++++--------------
 2 files changed, 43 insertions(+), 63 deletions(-)

diff --git a/examples/data/graphene_example.nc b/examples/data/graphene_example.nc
index 1b046e7f2ff0a5933df817865728b06780dd8fee..b779aefd53d518d3e385e9c75483c7a6251c1663 100644
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diff --git a/examples/graphene_extended_hubbard.ipynb b/examples/graphene_extended_hubbard.ipynb
index 71d40ec..e5aa8f6 100644
--- a/examples/graphene_extended_hubbard.ipynb
+++ b/examples/graphene_extended_hubbard.ipynb
@@ -23,8 +23,8 @@
    "source": [
     "Now we show the interface with `kwant`. We start by using `kwant` to build two tight-binding systems with translational symmetry:\n",
     "* graphene;\n",
-    "* a dummy system that encodes the interaction matrix.\n",
-    "See [`kwant_examples`](./codes/kwant_examples.py) to check how these two steps are done."
+    "* a dummy `kwant.Builder` that encodes the interaction matrix.\n",
+    "See [`kwant_examples`](./codes/kwant_examples.py) to verify how these two steps are done."
    ]
   },
   {
@@ -35,7 +35,7 @@
    "outputs": [],
    "source": [
     "# Create translationally-invariant `kwant.Builder`\n",
-    "bulk_graphene, syst_V = kwant_examples.graphene_extended_hubbard()"
+    "graphene_builder, int_builder = kwant_examples.graphene_extended_hubbard()"
    ]
   },
   {
@@ -43,7 +43,7 @@
    "id": "8f004476-fc3b-4c50-808c-4a636ce17c03",
    "metadata": {},
    "source": [
-    "We then use `utils.extract_hopping_vectors` to extract the hopping vectors of the `kwant.Builder` that encodes the interaction matrix."
+    "We then use `utils.builder2tb_model` to parse the `kwant.Builder` to a `tb_model` that we will use in the self-consistent calculations."
    ]
   },
   {
@@ -53,36 +53,7 @@
    "metadata": {},
    "outputs": [],
    "source": [
-    "tb_model = utils.builder2tb_model(bulk_graphene)"
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "id": "4a671249-a256-4e3f-b570-3ec10e5d9a40",
-   "metadata": {},
-   "source": [
-    "Finally, we use [`kwant.wraparound.wraparound`](https://kwant-project.org/doc/dev/reference/generated/kwant.wraparound.wraparound#kwant.wraparound.wraparound) to wrap the system."
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "id": "88183ab4-2f73-4389-a14f-168fe3806902",
-   "metadata": {},
-   "source": [
-    "With the finalized systems, we first generate an nd-array for the Hamiltonian evaluated on a $n \\times n$, $n=15$, k-point grid."
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 4,
-   "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",
-    "hamiltonians_0 = utils.kgrid_hamiltonian(nk, tb_model)"
+    "tb_model = utils.builder2tb_model(graphene_builder)"
    ]
   },
   {
@@ -90,12 +61,12 @@
    "id": "075df6f6-9311-4122-8b1e-2d709058e574",
    "metadata": {},
    "source": [
-    "Note that this grid is rather coarse, and thus not necessarily appropriate to observables. We thus use `utils.hk_densegrid` to compute the gap."
+    "Note that the self-consistent loop is performed on a coarse k-point grid, and thus not necessarily appropriate to compute observables. We thus use `utils.kgrid_hamiltonian` to evaluate the Hamiltonian on a denser k-point grid and compute the gap."
    ]
   },
   {
    "cell_type": "code",
-   "execution_count": 18,
+   "execution_count": 4,
    "id": "41bd9f60-8f29-4e7c-a0c4-a0bbf66445b2",
    "metadata": {},
    "outputs": [],
@@ -109,13 +80,14 @@
     "    filling=2,\n",
     "    guess=None,\n",
     "):\n",
+    "    scale = np.max(np.array([*tb_model.values()]))\n",
     "    # Generate guess on the same grid\n",
     "    if guess is None:\n",
-    "        guess = utils.generate_guess(nk, tb_model, int_model, scale=0.2)\n",
-    "    # else:\n",
-    "    #     guess += utils.generate_guess(\n",
-    "    #         nk, tb_model, int_model, scale=0.1 * np.max(np.abs(guess))\n",
-    "    #     )\n",
+    "        guess = utils.generate_guess(nk, tb_model, int_model, scale=scale)\n",
+    "    else:\n",
+    "        guess += utils.generate_guess(\n",
+    "            nk, tb_model, int_model, scale=scale\n",
+    "        )\n",
     "\n",
     "    # Find groundstate Hamiltonian on the same grid\n",
     "    mf_model, mf = hf.find_groundstate_ham(\n",
@@ -141,12 +113,12 @@
    "id": "718bc267-0899-4d45-8592-deabd6849a75",
    "metadata": {},
    "source": [
-    "Finally, we run the SCF by evaluating also the interacting matrix on a k-point grid."
+    "Finally, we also parse `int_builder` with the wanted interaction strength. Note that we pass a `params` dictionary to evaluate the Hamiltonian with `kwant`."
    ]
   },
   {
    "cell_type": "code",
-   "execution_count": 19,
+   "execution_count": 5,
    "id": "32b9e7c5-db12-44f9-930c-21e5494404b8",
    "metadata": {
     "tags": []
@@ -161,8 +133,8 @@
     "        for V in Vs:\n",
     "            params = dict(U=U, V=V)\n",
     "            _gap, guess = compute_gap(\n",
-    "                tb_model=utils.builder2tb_model(bulk_graphene),\n",
-    "                int_model=utils.builder2tb_model(syst_V, params),\n",
+    "                tb_model=tb_model,\n",
+    "                int_model=utils.builder2tb_model(int_builder, params),\n",
     "                nk=nk,\n",
     "                nk_dense=nk_dense,\n",
     "                guess=guess, U=U\n",
@@ -172,9 +144,17 @@
     "    return np.asarray(gap, dtype=float)"
    ]
   },
+  {
+   "cell_type": "markdown",
+   "id": "f1eba14e-e006-4162-885f-3302a92a21eb",
+   "metadata": {},
+   "source": [
+    "**Warning:** this phase diagram calculation takes about one hour."
+   ]
+  },
   {
    "cell_type": "code",
-   "execution_count": 20,
+   "execution_count": 6,
    "id": "6a8c08a9-7e31-420b-b6b4-709abfb26793",
    "metadata": {
     "tags": []
@@ -184,7 +164,7 @@
      "name": "stderr",
      "output_type": "stream",
      "text": [
-      "100%|██████████| 10/10 [03:45<00:00, 22.59s/it]\n"
+      "100%|██████████| 20/20 [53:16<00:00, 159.83s/it]\n"
      ]
     }
    ],
@@ -193,22 +173,14 @@
     "# Interaction strengths\n",
     "nk=15\n",
     "nk_dense=30\n",
-    "Us = np.linspace(0, 3, 10, endpoint=True)\n",
-    "Vs = np.linspace(0, 1.5, 10, endpoint=True)\n",
+    "Us = np.linspace(0, 3, 20, endpoint=True)\n",
+    "Vs = np.linspace(0, 1.5, 20, endpoint=True)\n",
     "gap = compute_phase_diagram(Us, Vs, nk=nk, nk_dense=nk_dense)"
    ]
   },
-  {
-   "cell_type": "markdown",
-   "id": "1f2defc7-d22b-4f12-834c-4ac8060da9c9",
-   "metadata": {},
-   "source": [
-    "We finally see two gapped regions in the spectrum. The bottom region is an antiferromagnetic groundstate, while the upper one is a charge density wave, as described in [arXiv:1204.4531](https://arxiv.org/abs/1204.4531)."
-   ]
-  },
   {
    "cell_type": "code",
-   "execution_count": 21,
+   "execution_count": 7,
    "id": "e17fc96c-c463-4e1f-8250-c254d761b92a",
    "metadata": {},
    "outputs": [],
@@ -217,25 +189,33 @@
     "gap_da = xr.DataArray(data=gap, coords=dict(Us=Us, Vs=Vs))"
    ]
   },
+  {
+   "cell_type": "markdown",
+   "id": "288f3d8e-8432-4697-be78-5156026f9fac",
+   "metadata": {},
+   "source": [
+    "We note that the gap openings coincide with the phase transitions from gapless to charge density wave or antiferromagnetic groundstates as predicted in [arXiv:1204.4531](https://arxiv.org/abs/1204.4531). "
+   ]
+  },
   {
    "cell_type": "code",
-   "execution_count": 23,
+   "execution_count": 8,
    "id": "101d04f3-f811-446d-a313-5a004eba2690",
    "metadata": {},
    "outputs": [
     {
      "data": {
       "text/plain": [
-       "<matplotlib.collections.QuadMesh at 0x7fe0ade2cad0>"
+       "<matplotlib.collections.QuadMesh at 0x7f946ef9d290>"
       ]
      },
-     "execution_count": 23,
+     "execution_count": 8,
      "metadata": {},
      "output_type": "execute_result"
     },
     {
      "data": {
-      "image/png": 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",
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",
       "text/plain": [
        "<Figure size 640x480 with 2 Axes>"
       ]
@@ -250,7 +230,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 25,
+   "execution_count": 9,
    "id": "0cb395cd-84d1-49b4-89dd-da7a2d09c8d0",
    "metadata": {},
    "outputs": [],
-- 
GitLab