Undo metadata changes

Author: Yue-Zhengyuan

docs/src/examples/hubbard_su/main.ipynb

@@ -1,17 +1,16 @@
 {
  "cells": [
   {
-   "cell_type": "code",
-   "execution_count": null,
-   "metadata": {},
    "outputs": [],
+   "cell_type": "code",
    "source": [
     "using Markdown #hide"
-   ]
+   ],
+   "metadata": {},
+   "execution_count": null
   },
   {
    "cell_type": "markdown",
-   "metadata": {},
    "source": [
     "# Simple update for the Fermi-Hubbard model at half-filling\n",
     "\n",
@@ -27,46 +26,46 @@
     "with $\\sigma \\in \\{\\uparrow,\\downarrow\\}$ and $n_{i,\\sigma} = c_{i,\\sigma}^+ c_{i,\\sigma}^-$.\n",
     "\n",
     "Let's get started by seeding the RNG and importing the required modules:"
-   ]
+   ],
+   "metadata": {}
   },
   {
-   "cell_type": "code",
-   "execution_count": null,
-   "metadata": {},
    "outputs": [],
+   "cell_type": "code",
    "source": [
     "using Random\n",
     "using TensorKit, PEPSKit\n",
     "Random.seed!(12329348592498);"
-   ]
+   ],
+   "metadata": {},
+   "execution_count": null
   },
   {
    "cell_type": "markdown",
-   "metadata": {},
    "source": [
     "## Defining the Hamiltonian\n",
     "\n",
     "First, we define the Hubbard model at $t=1$ hopping and $U=6$ using `Trivial` sectors for\n",
     "the particle and spin symmetries, and set $\\mu = U/2$ for half-filling. The model will be\n",
     "constructed on a $2 \\times 2$ unit cell, so we have:"
-   ]
+   ],
+   "metadata": {}
   },
   {
-   "cell_type": "code",
-   "execution_count": null,
-   "metadata": {},
    "outputs": [],
+   "cell_type": "code",
    "source": [
     "t = 1\n",
     "U = 6\n",
     "Nr, Nc = 2, 2\n",
     "H = hubbard_model(Float64, Trivial, Trivial, InfiniteSquare(Nr, Nc); t, U, mu = U / 2);\n",
     "physical_space = Vect[fℤ₂](0 => 2, 1 => 2);"
-   ]
+   ],
+   "metadata": {},
+   "execution_count": null
   },
   {
    "cell_type": "markdown",
-   "metadata": {},
    "source": [
     "## Running the simple update algorithm\n",
     "\n",
@@ -79,34 +78,33 @@
     "First, we shall use a small D for the random PEPS initialization, which is chosen as 4 here.\n",
     "For convenience, here we work with real tensors with `Float64` entries.\n",
     "The bond weights are still initialized as identity matrices."
-   ]
+   ],
+   "metadata": {}
   },
   {
-   "cell_type": "code",
-   "execution_count": null,
-   "metadata": {},
    "outputs": [],
+   "cell_type": "code",
    "source": [
     "virtual_space = Vect[fℤ₂](0 => 2, 1 => 2)\n",
     "peps = InfinitePEPS(rand, Float64, physical_space, virtual_space; unitcell = (Nr, Nc));\n",
     "wts = SUWeight(peps);"
-   ]
+   ],
+   "metadata": {},
+   "execution_count": null
   },
   {
    "cell_type": "markdown",
-   "metadata": {},
    "source": [
     "Starting from the random state, we first use a relatively large evolution time step\n",
     "`dt = 1e-2`. After convergence at D = 4, to avoid stucking at some bad local minimum,\n",
     "we first increase D to 12, and drop it back to D = 8 after a while.\n",
     "Afterwards, we keep D = 8 and gradually decrease `dt` to `1e-4` to improve convergence."
-   ]
+   ],
+   "metadata": {}
   },
   {
-   "cell_type": "code",
-   "execution_count": null,
-   "metadata": {},
    "outputs": [],
+   "cell_type": "code",
    "source": [
     "dts = [1.0e-2, 1.0e-2, 1.0e-3, 4.0e-4, 1.0e-4]\n",
     "tols = [1.0e-7, 1.0e-7, 1.0e-8, 1.0e-8, 1.0e-8]\n",
@@ -118,11 +116,12 @@
     "    alg = SimpleUpdate(; trunc, bipartite = false)\n",
     "    global peps, wts, = time_evolve(peps, H, dt, maxiter, alg, wts; tol, check_interval = 2000)\n",
     "end"
-   ]
+   ],
+   "metadata": {},
+   "execution_count": null
   },
   {
    "cell_type": "markdown",
-   "metadata": {},
    "source": [
     "## Computing the ground-state energy\n",
     "\n",
@@ -131,13 +130,12 @@
     "which is initialized using the simple update bond weights. Next we use it to initialize\n",
     "another run with bigger environment dimension. The dynamic adjustment of environment dimension\n",
     "is achieved by using `trunc=truncrank(χ)` with different `χ`s in the CTMRG runs:"
-   ]
+   ],
+   "metadata": {}
   },
   {
-   "cell_type": "code",
-   "execution_count": null,
-   "metadata": {},
    "outputs": [],
+   "cell_type": "code",
    "source": [
     "χenv₀, χenv = 6, 16\n",
     "env_space = Vect[fℤ₂](0 => χenv₀ / 2, 1 => χenv₀ / 2)\n",
@@ -148,69 +146,71 @@
     "        env, peps; alg = :sequential, tol = 1.0e-8, maxiter = 50, trunc = truncrank(χ)\n",
     "    )\n",
     "end"
-   ]
+   ],
+   "metadata": {},
+   "execution_count": null
   },
   {
    "cell_type": "markdown",
-   "metadata": {},
    "source": [
     "We measure the energy by computing the `H` expectation value, where we have to make sure to\n",
     "normalize with respect to the unit cell to obtain the energy per site:"
-   ]
+   ],
+   "metadata": {}
   },
   {
-   "cell_type": "code",
-   "execution_count": null,
-   "metadata": {},
    "outputs": [],
+   "cell_type": "code",
    "source": [
     "E = expectation_value(peps, H, env) / (Nr * Nc)\n",
     "@show E;"
-   ]
+   ],
+   "metadata": {},
+   "execution_count": null
   },
   {
    "cell_type": "markdown",
-   "metadata": {},
    "source": [
     "Finally, we can compare the obtained ground-state energy against the literature, namely the\n",
     "QMC estimates from [Qin et al.](@cite qin_benchmark_2016). We find that the results generally\n",
     "agree:"
-   ]
+   ],
+   "metadata": {}
   },
   {
-   "cell_type": "code",
-   "execution_count": null,
-   "metadata": {},
    "outputs": [],
+   "cell_type": "code",
    "source": [
     "Es_exact = Dict(0 => -1.62, 2 => -0.176, 4 => 0.8603, 6 => -0.6567, 8 => -0.5243)\n",
     "E_exact = Es_exact[U] - U / 2\n",
     "@show (E - E_exact) / abs(E_exact);"
-   ]
+   ],
+   "metadata": {},
+   "execution_count": null
   },
   {
    "cell_type": "markdown",
-   "metadata": {},
    "source": [
     "---\n",
     "\n",
     "*This notebook was generated using [Literate.jl](https://github.com/fredrikekre/Literate.jl).*"
-   ]
+   ],
+   "metadata": {}
   }
  ],
+ "nbformat_minor": 3,
  "metadata": {
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-   "display_name": "Julia 1.11.7",
-   "language": "julia",
-   "name": "julia-1.11"
-  },
   "language_info": {
    "file_extension": ".jl",
    "mimetype": "application/julia",
    "name": "julia",
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+  },
+  "kernelspec": {
+   "name": "julia-1.11",
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- "nbformat": 4,
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+ "nbformat": 4
+}