{ "cells": [ { "cell_type": "markdown", "id": "43da1168-b444-4dd6-b0cb-40d2ea7d819f", "metadata": {}, "source": [ "(real-time-simple-update)=\n", "\n", "# Real time simple update (SU)" ] }, { "cell_type": "code", "execution_count": 1, "id": "20a665ab-9aef-4e19-b3e2-168fd53c77c2", "metadata": {}, "outputs": [], "source": [ "%config InlineBackend.figure_formats = ['svg']\n", "import autoray as ar\n", "import matplotlib as mpl\n", "import matplotlib.pyplot as plt\n", "import tqdm # for progress bar\n", "\n", "import quimb as qu\n", "import quimb.tensor as qtn\n", "\n", "mpl.style.use(qu.NEUTRAL_STYLE)" ] }, { "cell_type": "code", "execution_count": 2, "id": "4ddbbf97-1c89-4cce-8eac-dfb3d1bda235", "metadata": {}, "outputs": [], "source": [ "Lx = 11\n", "Ly = 11\n", "\n", "edges = qtn.edges_2d_square(Lx, Ly, cyclic=False)\n", "sites = sorted({s for e in edges for s in e})\n", "\n", "# heisenberg interaction\n", "h2 = -qu.pauli(\"X\") & qu.pauli(\"X\")\n", "# quenched random onsite z-fields\n", "h1 = -3.04438 * qu.pauli(\"Z\")" ] }, { "cell_type": "code", "execution_count": 3, "id": "74f52899-8450-4cb6-8960-5eaba3dd20f2", "metadata": {}, "outputs": [ { "data": { "text/html": [ "TensorNetworkGenVector(tensors=121, indices=341)Tensor(shape=(1, 1, 2), inds=[_3a1604AAAAB, _3a1604AAAAA, k(0, 0)], tags={I(0, 0)}),backend=numpy, dtype=float64, data=array([[[1., 0.]]])Tensor(shape=(1, 1, 1, 2), inds=[_3a1604AAAAD, _3a1604AAAAC, _3a1604AAAAA, k(0, 1)], tags={I(0, 1)}),backend=numpy, dtype=float64, data=array([[[[1., 0.]]]])Tensor(shape=(1, 1, 1, 2), inds=[_3a1604AAAAF, _3a1604AAAAE, _3a1604AAAAC, k(0, 2)], tags={I(0, 2)}),backend=numpy, dtype=float64, data=array([[[[1., 0.]]]])Tensor(shape=(1, 1, 1, 2), inds=[_3a1604AAAAH, _3a1604AAAAG, _3a1604AAAAE, k(0, 3)], tags={I(0, 3)}),backend=numpy, dtype=float64, data=array([[[[1., 0.]]]])Tensor(shape=(1, 1, 1, 2), inds=[_3a1604AAAAJ, _3a1604AAAAI, _3a1604AAAAG, k(0, 4)], tags={I(0, 4)}),backend=numpy, dtype=float64, 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2), inds=[_3a1604AAADi, _3a1604AAADh, _3a1604AAADN, k(9, 0)], tags={I(9, 0)}),backend=numpy, dtype=float64, data=array([[[[1., 0.]]]])..." ], "text/plain": [ "TensorNetworkGenVector(tensors=121, indices=341)" ] }, "execution_count": 4, "metadata": {}, "output_type": "execute_result" } ], "source": [ "# create simple update gauges\n", "gauges = {}\n", "psi.gauge_all_simple_(gauges=gauges)" ] }, { "cell_type": "code", "execution_count": 5, "id": "3089c388-78a3-4204-ab12-beae05070536", "metadata": {}, "outputs": [], "source": [ "results = {}\n", "\n", "# truncation options\n", "max_bond = 16\n", "cutoff = 1e-6\n", "\n", "t = 0.0\n", "dt = 0.04\n", "\n", "U2 = ar.do(\"linalg.expm\", -1j * dt * h2)\n", "U1 = ar.do(\"linalg.expm\", -1j * dt * h1)" ] }, { "cell_type": "code", "execution_count": 6, "id": "f89821a4-4e10-4cfa-82b4-29081f41b4c8", "metadata": {}, "outputs": [], "source": [ "mag_terms = {(site,): qu.pauli(\"Z\") for site in [(Lx // 2, Ly // 2)]}\n", "\n", "cluster_sets = {c: tuple(psi.gen_gloops_sites(c)) for c in [0, 4, 6]}" ] }, { "cell_type": "code", "execution_count": 7, "id": "4f636b90-e0f0-446f-a292-ec7c35b896f0", "metadata": {}, "outputs": [ { "data": { "text/plain": [ "[0, 100, 280]" ] }, "execution_count": 7, "metadata": {}, "output_type": "execute_result" } ], "source": [ "[len(cs) for cs in cluster_sets.values()]" ] }, { "cell_type": "code", "execution_count": 8, "id": "91dfbbb7-131d-4206-9cd9-99de6303411d", "metadata": {}, "outputs": [], "source": [ "def measure():\n", " if \"times\" in results and results[\"times\"][-1] == t:\n", " # already measured this time\n", " return\n", "\n", " results.setdefault(\"times\", []).append(t)\n", "\n", " for c, gloops in cluster_sets.items():\n", " results.setdefault((\"norm\", c), []).append(\n", " psi.norm_gloop_expand(\n", " gauges=gauges,\n", " gloops=gloops,\n", " optimize=\"random-greedy\",\n", " autocomplete=True,\n", " autoreduce=True,\n", " ).real\n", " )\n", "\n", " # store some intermediate state for efficiency\n", " info = {}\n", " for c, gloops in cluster_sets.items():\n", " results.setdefault((\"mag\", c), []).append(\n", " psi.compute_local_expectation_gloop_expand(\n", " mag_terms,\n", " gauges=gauges,\n", " normalized=\"prod\",\n", " gloops=gloops,\n", " optimize=\"random-greedy\",\n", " autocomplete=True,\n", " info=info,\n", " ).real\n", " / len(mag_terms)\n", " )" ] }, { "cell_type": "code", "execution_count": 12, "id": "f44d6063-d39d-4b1a-b295-f43b3fe07ac7", "metadata": {}, "outputs": [ { "name": "stderr", "output_type": "stream", "text": [ "100%|███████████████████████████████████████████████████████████████████████████| 10/10 [11:32<00:00, 69.24s/it]\n" ] } ], "source": [ "for i in tqdm.trange(10):\n", " measure()\n", "\n", " for edge in qtn.tnag.tebd.edge_coloring(\n", " edges,\n", " \"random_sequential\",\n", " group=False,\n", " ):\n", " psi.gate_simple_(\n", " U2,\n", " where=edge,\n", " gauges=gauges,\n", " max_bond=max_bond,\n", " cutoff=cutoff,\n", " renorm=False,\n", " )\n", "\n", " for site in sites:\n", " psi.gate_simple_(U1, (site,), gauges=gauges)\n", "\n", " # ensure gauge is equilibrated\n", " psi.gauge_all_simple_(\n", " max_iterations=1000,\n", " tol=1e-6,\n", " gauges=gauges,\n", " progbar=False,\n", " )\n", "\n", " t += dt\n", "\n", "measure()" ] }, { "cell_type": "code", "execution_count": 13, "id": "aa195323-1c15-4030-a2f4-720b4360a4a7", "metadata": {}, "outputs": [ { "data": { "text/html": [ "TensorNetworkGenVector(tensors=121, indices=341)Tensor(shape=(16, 16, 2), inds=[_7322eeAAAAB, _7322eeAAAAA, k(0, 0)], tags={I(0, 0)}),backend=numpy, dtype=complex128, data=...Tensor(shape=(16, 16, 16, 2), inds=[_7322eeAAAAD, _7322eeAAAAC, _7322eeAAAAA, k(0, 1)], tags={I(0, 1)}),backend=numpy, dtype=complex128, data=...Tensor(shape=(16, 16, 16, 2), inds=[_7322eeAAAAF, _7322eeAAAAE, _7322eeAAAAC, k(0, 2)], tags={I(0, 2)}),backend=numpy, dtype=complex128, data=...Tensor(shape=(16, 16, 16, 2), inds=[_7322eeAAAAH, _7322eeAAAAG, 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inds=[_7322eeAAADf, _7322eeAAADe, _7322eeAAADc, _7322eeAAADK, k(8, 9)], tags={I(8, 9)}),backend=numpy, dtype=complex128, data=...Tensor(shape=(16, 16, 16, 2), inds=[_7322eeAAADg, _7322eeAAADe, _7322eeAAADL, k(8, 10)], tags={I(8, 10)}),backend=numpy, dtype=complex128, data=...Tensor(shape=(16, 16, 16, 2), inds=[_7322eeAAADi, _7322eeAAADh, _7322eeAAADN, k(9, 0)], tags={I(9, 0)}),backend=numpy, dtype=complex128, data=......" ], "text/plain": [ "TensorNetworkGenVector(tensors=121, indices=341)" ] }, "execution_count": 13, "metadata": {}, "output_type": "execute_result" } ], "source": [ "psi" ] }, { "cell_type": "code", "execution_count": 14, "id": "ed33fe6b-4ecd-46c8-bf3d-d775b2f970d3", "metadata": {}, "outputs": [ { "data": { "image/svg+xml": [ "" ], "text/plain": [ "" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "for i, c in enumerate(cluster_sets):\n", " plt.plot(\n", " results[\"times\"],\n", " results[\"norm\", c],\n", " \".-\",\n", " label=f\"C{c}\",\n", " color=mpl.cm.Blues((i + 1) / len(cluster_sets)),\n", " linewidth=2 * (i + 1) / len(cluster_sets),\n", " )\n", "\n", "for i, c in enumerate(cluster_sets):\n", " plt.plot(\n", " results[\"times\"],\n", " results[\"mag\", c],\n", " \"|-\",\n", " label=f\"C{c}\",\n", " color=mpl.cm.Greens((i + 1) / len(cluster_sets)),\n", " linewidth=2 * (i + 1) / len(cluster_sets),\n", " )\n", "\n", "plt.legend(bbox_to_anchor=(1, 1))\n", "plt.show()\n", "plt.close()" ] } ], "metadata": { "kernelspec": { "display_name": "Python 3", "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" } }, "nbformat": 4, "nbformat_minor": 4 }
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