{ "cells": [ { "cell_type": "markdown", "source": [ "# Gross-Pitaevskii equation with magnetism" ], "metadata": {} }, { "cell_type": "markdown", "source": [ "We solve the 2D Gross-Pitaevskii equation with a magnetic field.\n", "This is similar to the\n", "previous example (Gross-Pitaevskii equation in one dimension),\n", "but with an extra term for the magnetic field.\n", "We reproduce here the results of https://arxiv.org/pdf/1611.02045.pdf Fig. 10" ], "metadata": {} }, { "outputs": [], "cell_type": "code", "source": [ "using DFTK\n", "using StaticArrays\n", "using Plots" ], "metadata": {}, "execution_count": 1 }, { "cell_type": "markdown", "source": [ "Unit cell. Having one of the lattice vectors as zero means a 2D system" ], "metadata": {} }, { "outputs": [], "cell_type": "code", "source": [ "a = 15\n", "lattice = a .* [[1 0 0.]; [0 1 0]; [0 0 0]];" ], "metadata": {}, "execution_count": 2 }, { "cell_type": "markdown", "source": [ "Confining scalar potential, and magnetic vector potential" ], "metadata": {} }, { "outputs": [], "cell_type": "code", "source": [ "pot(x, y, z) = ((x - a/2)^2 + (y - a/2)^2)/2\n", "ω = .6\n", "Apot(x, y, z) = ω * @SVector [y - a/2, -(x - a/2), 0]\n", "Apot(X) = Apot(X...);" ], "metadata": {}, "execution_count": 3 }, { "cell_type": "markdown", "source": [ "Parameters" ], "metadata": {} }, { "outputs": [], "cell_type": "code", "source": [ "Ecut = 20 # Increase this for production\n", "η = 500\n", "C = η/2\n", "α = 2\n", "n_electrons = 1; # Increase this for fun" ], "metadata": {}, "execution_count": 4 }, { "cell_type": "markdown", "source": [ "Collect all the terms, build and run the model" ], "metadata": {} }, { "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Iter Function value Gradient norm \n", " 0 3.159302e+01 7.954240e+00\n", " * time: 0.002009868621826172\n", " 1 2.780263e+01 4.201989e+00\n", " * time: 0.008098840713500977\n", " 2 1.844724e+01 3.927732e+00\n", " * time: 0.013222932815551758\n", " 3 1.179513e+01 2.401116e+00\n", " * time: 0.01809096336364746\n", " 4 1.176026e+01 3.197918e+00\n", " * time: 0.021857023239135742\n", " 5 1.067411e+01 2.006407e+00\n", " * time: 0.025758028030395508\n", " 6 9.876183e+00 1.644597e+00\n", " * time: 0.08055496215820312\n", " 7 9.267052e+00 1.386918e+00\n", " * time: 0.08441281318664551\n", " 8 8.693555e+00 1.211421e+00\n", " * time: 0.08846282958984375\n", " 9 8.313659e+00 5.763612e-01\n", " * time: 0.09302282333374023\n", " 10 8.111231e+00 3.628822e-01\n", " * time: 0.09696197509765625\n", " 11 8.070203e+00 8.309101e-01\n", " * time: 0.10015082359313965\n", " 12 8.013909e+00 6.662059e-01\n", " * time: 0.10308980941772461\n", " 13 7.964668e+00 5.244057e-01\n", " * time: 0.10687994956970215\n", " 14 7.918505e+00 6.537759e-01\n", " * time: 0.11037087440490723\n", " 15 7.882190e+00 6.176930e-01\n", " * time: 0.11362695693969727\n", " 16 7.861291e+00 5.792358e-01\n", " * time: 0.11765003204345703\n", " 17 7.857775e+00 8.097500e-01\n", " * time: 0.12124991416931152\n", " 18 7.848050e+00 5.014490e-01\n", " * time: 0.12543487548828125\n", " 19 7.840127e+00 5.779733e-01\n", " * time: 0.1297929286956787\n", " 20 7.824555e+00 4.517695e-01\n", " * time: 0.13374900817871094\n", " 21 7.794490e+00 3.513582e-01\n", " * time: 0.13894295692443848\n", " 22 7.757036e+00 3.081699e-01\n", " * time: 0.14368200302124023\n", " 23 7.734985e+00 3.045205e-01\n", " * time: 0.14804697036743164\n", " 24 7.718664e+00 2.388876e-01\n", " * time: 0.15254592895507812\n", " 25 7.705537e+00 2.366791e-01\n", " * time: 0.15892481803894043\n", " 26 7.692254e+00 1.739177e-01\n", " * time: 0.16576004028320312\n", " 27 7.683319e+00 1.584658e-01\n", " * time: 0.1727449893951416\n", " 28 7.677054e+00 1.507266e-01\n", " * time: 0.17956280708312988\n", " 29 7.672841e+00 1.055739e-01\n", " * time: 0.1869640350341797\n", " 30 7.668999e+00 9.682580e-02\n", " * time: 0.19370388984680176\n", " 31 7.668828e+00 2.076956e-01\n", " * time: 0.19881796836853027\n", " 32 7.666279e+00 1.110749e-01\n", " * time: 0.20399904251098633\n", " 33 7.662265e+00 8.720288e-02\n", " * time: 0.20971393585205078\n", " 34 7.657904e+00 8.038331e-02\n", " * time: 0.21512484550476074\n", " 35 7.654586e+00 7.594841e-02\n", " * time: 0.2205049991607666\n", " 36 7.651832e+00 1.043558e-01\n", " * time: 0.2258739471435547\n", " 37 7.651782e+00 1.814430e-01\n", " * time: 0.23126792907714844\n", " 38 7.651068e+00 1.309087e-01\n", " * time: 0.23656702041625977\n", " 39 7.648804e+00 8.965576e-02\n", " * time: 0.2410259246826172\n", " 40 7.647562e+00 1.303120e-01\n", " * time: 0.27387499809265137\n", " 41 7.646463e+00 1.290807e-01\n", " * time: 0.2770049571990967\n", " 42 7.644676e+00 6.908459e-02\n", " * time: 0.2811448574066162\n", " 43 7.643080e+00 6.639827e-02\n", " * time: 0.28412604331970215\n", " 44 7.642016e+00 9.022525e-02\n", " * time: 0.2871739864349365\n", " 45 7.641164e+00 7.792273e-02\n", " * time: 0.29041194915771484\n", " 46 7.640939e+00 7.791173e-02\n", " * time: 0.294003963470459\n", " 47 7.640468e+00 6.759223e-02\n", " * time: 0.29709887504577637\n", " 48 7.639373e+00 6.334034e-02\n", " * time: 0.301088809967041\n", " 49 7.639336e+00 1.203100e-01\n", " * time: 0.3041689395904541\n", " 50 7.638557e+00 7.425392e-02\n", " * time: 0.3071858882904053\n", " 51 7.638444e+00 1.192827e-01\n", " * time: 0.3139069080352783\n", " 52 7.637401e+00 6.461574e-02\n", " * time: 0.3180990219116211\n", " 53 7.636460e+00 6.890534e-02\n", " * time: 0.32116198539733887\n", " 54 7.636328e+00 1.082896e-01\n", " * time: 0.32561802864074707\n", " 55 7.636240e+00 9.020901e-02\n", " * time: 0.33007192611694336\n", " 56 7.635659e+00 8.720103e-02\n", " * time: 0.33474183082580566\n", " 57 7.634665e+00 7.511869e-02\n", " * time: 0.3385770320892334\n", " 58 7.634052e+00 1.004545e-01\n", " * time: 0.3418450355529785\n", " 59 7.633051e+00 9.960058e-02\n", " * time: 0.3453710079193115\n", " 60 7.631484e+00 7.833726e-02\n", " * time: 0.34929490089416504\n", " 61 7.631166e+00 1.032684e-01\n", " * time: 0.3528900146484375\n", " 62 7.630135e+00 6.785583e-02\n", " * time: 0.35856199264526367\n", " 63 7.629366e+00 7.404326e-02\n", " * time: 0.3621039390563965\n", " 64 7.628062e+00 5.742880e-02\n", " * time: 0.3652470111846924\n", " 65 7.626807e+00 5.870567e-02\n", " * time: 0.3690769672393799\n", " 66 7.625676e+00 4.600444e-02\n", " * time: 0.3733029365539551\n", " 67 7.625311e+00 5.860455e-02\n", " * time: 0.37666893005371094\n", " 68 7.625202e+00 8.044384e-02\n", " * time: 0.37981486320495605\n", " 69 7.624505e+00 7.451637e-02\n", " * time: 0.3832108974456787\n", " 70 7.623780e+00 5.906647e-02\n", " * time: 0.38716697692871094\n", " 71 7.623195e+00 6.250966e-02\n", " * time: 0.3905489444732666\n", " 72 7.622122e+00 5.222588e-02\n", " * time: 0.3939328193664551\n", " 73 7.621521e+00 4.825247e-02\n", " * time: 0.3981039524078369\n", " 74 7.621401e+00 6.166178e-02\n", " * time: 0.4238569736480713\n", " 75 7.621026e+00 7.264602e-02\n", " * time: 0.42705202102661133\n", " 76 7.620596e+00 4.512260e-02\n", " * time: 0.4309418201446533\n", " 77 7.620242e+00 4.078696e-02\n", " * time: 0.4354228973388672\n", " 78 7.619790e+00 6.124635e-02\n", " * time: 0.4388718605041504\n", " 79 7.619088e+00 2.700327e-02\n", " * time: 0.4429128170013428\n", " 80 7.618657e+00 3.571521e-02\n", " * time: 0.44611597061157227\n", " 81 7.618261e+00 3.572477e-02\n", " * time: 0.44927287101745605\n", " 82 7.617977e+00 3.869710e-02\n", " * time: 0.4524409770965576\n", " 83 7.617864e+00 5.379989e-02\n", " * time: 0.4558110237121582\n", " 84 7.617623e+00 3.964675e-02\n", " * time: 0.45918703079223633\n", " 85 7.617367e+00 5.980302e-02\n", " * time: 0.46233701705932617\n", " 86 7.617175e+00 5.003426e-02\n", " * time: 0.4653019905090332\n", " 87 7.616841e+00 3.962685e-02\n", " * time: 0.4692239761352539\n", " 88 7.616767e+00 6.209490e-02\n", " * time: 0.4726858139038086\n", " 89 7.616384e+00 4.306300e-02\n", " * time: 0.4757578372955322\n", " 90 7.616216e+00 5.521380e-02\n", " * time: 0.4792978763580322\n", " 91 7.615980e+00 4.927200e-02\n", " * time: 0.48257899284362793\n", " 92 7.615740e+00 3.535453e-02\n", " * time: 0.48575401306152344\n", " 93 7.615676e+00 5.091764e-02\n", " * time: 0.4891040325164795\n", " 94 7.615635e+00 5.922005e-02\n", " * time: 0.4926269054412842\n", " 95 7.615382e+00 3.365309e-02\n", " * time: 0.49715185165405273\n", " 96 7.615225e+00 4.059725e-02\n", " * time: 0.5007200241088867\n", " 97 7.614919e+00 3.376194e-02\n", " * time: 0.5052328109741211\n", " 98 7.614778e+00 6.411183e-02\n", " * time: 0.5083239078521729\n", " 99 7.614484e+00 3.135854e-02\n", " * time: 0.513124942779541\n", " 100 7.614367e+00 3.038978e-02\n", " * time: 0.5160679817199707\n", " 101 7.614215e+00 3.256369e-02\n", " * time: 0.5201749801635742\n", " 102 7.614127e+00 3.432930e-02\n", " * time: 0.5234129428863525\n", " 103 7.614009e+00 3.052841e-02\n", " * time: 0.526453971862793\n", " 104 7.613897e+00 4.097112e-02\n", " * time: 0.5294768810272217\n", " 105 7.613811e+00 3.884824e-02\n", " * time: 0.5325348377227783\n", " 106 7.613644e+00 3.899195e-02\n", " * time: 0.5359549522399902\n", " 107 7.613528e+00 3.106242e-02\n", " * time: 0.5393610000610352\n", " 108 7.613366e+00 3.288238e-02\n", " * time: 0.5520198345184326\n", " 109 7.613356e+00 4.421898e-02\n", " * time: 0.555513858795166\n", " 110 7.613263e+00 3.957131e-02\n", " * time: 0.5582869052886963\n", " 111 7.613135e+00 4.413959e-02\n", " * time: 0.5611448287963867\n", " 112 7.613004e+00 2.652923e-02\n", " * time: 0.5642340183258057\n", " 113 7.612972e+00 4.891870e-02\n", " * time: 0.5671529769897461\n", " 114 7.612966e+00 3.703895e-02\n", " * time: 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"output_type": "execute_result", "data": { "text/plain": "Plot{Plots.GRBackend() n=1}", "image/png": 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n_electrons=n_electrons,\n", " terms=terms, spin_polarization=:spinless) # \"spinless electrons\"\n", "basis = PlaneWaveBasis(model, Ecut, kgrid=(1, 1, 1))\n", "scfres = direct_minimization(basis, tol=1e-5) # Reduce tol for production\n", "heatmap(scfres.ρ.real[:, :, 1], c=:blues)" ], "metadata": {}, "execution_count": 5 } ], "nbformat_minor": 3, "metadata": { "language_info": { "file_extension": ".jl", "mimetype": "application/julia", "name": "julia", "version": "1.6.0" }, "kernelspec": { "name": "julia-1.6", "display_name": "Julia 1.6.0", "language": "julia" } }, "nbformat": 4 }