{
"cells": [
{
"cell_type": "markdown",
"source": [
"# Anyonic models"
],
"metadata": {}
},
{
"cell_type": "markdown",
"source": [
"We solve the almost-bosonic anyon model of https://arxiv.org/pdf/1901.10739.pdf"
],
"metadata": {}
},
{
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"n Energy log10(ΔE) log10(Δρ) Δtime\n",
"--- --------------- --------- --------- ------\n",
" 1 +64.36949742807 -2.49 6.13s\n",
" 2 +58.27460242935 0.78 -1.39 72.7ms\n",
" 3 +42.75547208388 1.19 -1.01 14.3ms\n",
" 4 +32.72182473424 1.00 -0.87 40.0ms\n",
" 5 +28.65270254117 0.61 -0.76 12.3ms\n",
" 6 +13.62042284706 1.18 -0.71 16.1ms\n",
" 7 +12.88111147864 -0.13 -0.91 8.53ms\n",
" 8 +10.92717077925 0.29 -0.63 14.1ms\n",
" 9 +9.334307576085 0.20 -0.67 13.8ms\n",
" 10 +7.680212136437 0.22 -0.73 13.8ms\n",
" 11 +6.919436428620 -0.12 -0.66 8.65ms\n",
" 12 +6.389827978826 -0.28 -0.68 12.0ms\n",
" 13 +6.207808846761 -0.74 -0.76 11.9ms\n",
" 14 +6.090523098309 -0.93 -0.77 8.83ms\n",
" 15 +5.954415594367 -0.87 -0.83 12.0ms\n",
" 16 +5.944013546273 -1.98 -0.88 6.68ms\n",
" 17 +5.892941365545 -1.29 -0.90 9.89ms\n",
" 18 +5.826726255386 -1.18 -0.95 6.83ms\n",
" 19 +5.745943672255 -1.09 -0.99 9.91ms\n",
" 20 +5.707653718832 -1.42 -1.01 8.54ms\n",
" 21 +5.659841885200 -1.32 -0.85 11.8ms\n",
" 22 +5.632943051951 -1.57 -1.00 11.7ms\n",
" 23 +5.607223982781 -1.59 -1.25 6.80ms\n",
" 24 +5.595945709876 -1.95 -1.22 11.8ms\n",
" 25 +5.588827308814 -2.15 -1.27 8.57ms\n",
" 26 +5.580525271263 -2.08 -1.36 11.8ms\n",
" 27 +5.571857154876 -2.06 -1.50 6.70ms\n",
" 28 +5.568465971100 -2.47 -1.24 9.93ms\n",
" 29 +5.567657317603 -3.09 -1.57 6.63ms\n",
" 30 +5.565756121210 -2.72 -1.82 9.79ms\n",
" 31 +5.565038182986 -3.14 -1.81 6.63ms\n",
" 32 +5.563665466976 -2.86 -1.60 11.8ms\n",
" 33 +5.562528860565 -2.94 -1.72 11.8ms\n",
" 34 +5.560377725829 -2.67 -1.76 6.83ms\n",
" 35 +5.559276863161 -2.96 -1.70 11.8ms\n",
" 36 +5.558900469181 -3.42 -1.86 6.72ms\n",
" 37 +5.558524933287 -3.43 -1.85 11.8ms\n",
" 38 +5.557951739196 -3.24 -1.72 6.66ms\n",
" 39 +5.557832976259 -3.93 -1.82 9.92ms\n",
" 40 +5.556855126483 -3.01 -1.83 6.73ms\n",
" 41 +5.555854816213 -3.00 -1.63 9.84ms\n",
" 42 +5.554582532236 -2.90 -1.19 6.69ms\n",
" 43 +5.549979991108 -2.34 -1.34 9.92ms\n",
" 44 +5.549594975354 -3.41 -0.83 6.75ms\n",
" 45 +5.547443001357 -2.67 -0.74 9.78ms\n",
" 46 +5.537982479542 -2.02 -0.68 8.64ms\n",
" 47 +5.528001898549 -2.00 -0.68 12.0ms\n",
" 48 +5.500301552405 -1.56 -0.58 8.74ms\n",
" 49 +5.480504836116 -1.70 -0.64 12.0ms\n",
" 50 +5.462094303668 -1.73 -0.67 11.8ms\n",
" 51 +5.433076189719 -1.54 -0.78 8.52ms\n",
" 52 +5.375713620894 -1.24 -0.69 11.8ms\n",
" 53 +5.339099116652 -1.44 -0.75 11.9ms\n",
" 54 +5.299007602051 -1.40 -0.85 8.60ms\n",
" 55 +5.268589761222 -1.52 -0.71 11.8ms\n",
" 56 +5.230538071352 -1.42 -0.66 8.63ms\n",
" 57 +5.200569989734 -1.52 -0.69 11.8ms\n",
" 58 +5.186201854578 -1.84 -0.67 11.6ms\n",
" 59 +5.178026122302 -2.09 -0.60 8.62ms\n",
" 60 +5.166705937078 -1.95 -0.69 11.7ms\n",
" 61 +5.159235757399 -2.13 -0.92 6.68ms\n",
" 62 +5.150561361500 -2.06 -0.73 11.8ms\n",
" 63 +5.142022328686 -2.07 -0.81 11.7ms\n",
" 64 +5.131878680754 -1.99 -0.78 8.70ms\n",
" 65 +5.125306712830 -2.18 -0.80 11.8ms\n",
" 66 +5.117754240311 -2.12 -0.89 11.6ms\n",
" 67 +5.108754060644 -2.05 -0.80 8.76ms\n",
" 68 +5.101050315837 -2.11 -0.76 11.9ms\n",
" 69 +5.093934098088 -2.15 -0.78 8.55ms\n",
" 70 +5.086316484253 -2.12 -0.74 12.0ms\n",
" 71 +5.075851161539 -1.98 -0.82 11.6ms\n",
" 72 +5.062946042065 -1.89 -0.70 8.67ms\n",
" 73 +5.049776569998 -1.88 -0.70 11.9ms\n",
" 74 +5.036114281197 -1.86 -0.70 11.6ms\n",
" 75 +5.021672160622 -1.84 -0.67 8.74ms\n",
" 76 +5.008058393962 -1.87 -0.66 12.0ms\n",
" 77 +4.996245868626 -1.93 -0.65 8.66ms\n",
" 78 +4.986162664338 -2.00 -0.67 11.9ms\n",
" 79 +4.977846698493 -2.08 -0.71 11.8ms\n",
" 80 +4.968023636162 -2.01 -0.69 8.68ms\n",
" 81 +4.957119226039 -1.96 -0.68 11.8ms\n",
" 82 +4.945097415211 -1.92 -0.65 8.52ms\n",
" 83 +4.922012929261 -1.64 -0.57 11.8ms\n",
" 84 +4.903536885185 -1.73 -0.61 11.7ms\n",
" 85 +4.872822998541 -1.51 -0.68 8.60ms\n",
" 86 +4.855520432095 -1.76 -0.74 11.8ms\n",
" 87 +4.834607441567 -1.68 -0.78 11.8ms\n",
" 88 +4.819736764542 -1.83 -0.75 8.62ms\n",
" 89 +4.809283086474 -1.98 -0.83 11.9ms\n",
" 90 +4.800138687829 -2.04 -0.84 8.54ms\n",
" 91 +4.792276413720 -2.10 -0.86 11.6ms\n",
" 92 +4.784736826280 -2.12 -0.86 11.7ms\n",
" 93 +4.779688310993 -2.30 -0.93 6.67ms\n",
" 94 +4.770099838134 -2.02 -0.81 11.9ms\n",
" 95 +4.763014950498 -2.15 -0.68 8.62ms\n",
" 96 +4.748364517153 -1.83 -0.63 12.1ms\n",
" 97 +4.741930961418 -2.19 -0.70 29.8ms\n",
" 98 +4.736145228996 -2.24 -1.17 6.93ms\n",
" 99 +4.728828738111 -2.14 -0.99 12.0ms\n",
" 100 +4.722858671743 -2.22 -1.14 8.51ms\n",
" 101 +4.716337310643 -2.19 -1.06 11.7ms\n",
" 102 +4.712169918229 -2.38 -0.94 11.7ms\n",
" 103 +4.709036010736 -2.50 -0.92 8.67ms\n",
" 104 +4.705871059790 -2.50 -0.95 11.6ms\n",
" 105 +4.703398638534 -2.61 -0.96 8.56ms\n",
" 106 +4.700141117206 -2.49 -0.96 11.8ms\n",
" 107 +4.695721177212 -2.35 -0.92 11.7ms\n",
" 108 +4.692035292275 -2.43 -0.84 8.61ms\n",
" 109 +4.687819958886 -2.38 -0.91 11.8ms\n",
" 110 +4.683794280151 -2.40 -0.81 11.7ms\n",
" 111 +4.679577650317 -2.38 -0.77 8.62ms\n",
" 112 +4.675646356510 -2.41 -0.77 11.9ms\n",
" 113 +4.673253557760 -2.62 -0.93 8.52ms\n",
" 114 +4.670612244034 -2.58 -0.99 11.7ms\n",
" 115 +4.667159396724 -2.46 -0.85 11.8ms\n",
" 116 +4.665245443918 -2.72 -0.89 8.55ms\n",
" 117 +4.663234598496 -2.70 -1.04 11.9ms\n",
" 118 +4.661719188026 -2.82 -0.81 11.8ms\n",
" 119 +4.660864167439 -3.07 -0.95 8.61ms\n",
" 120 +4.660136295826 -3.14 -1.20 11.8ms\n",
" 121 +4.659229474186 -3.04 -1.22 8.62ms\n",
" 122 +4.658174908941 -2.98 -0.94 11.9ms\n",
" 123 +4.657206678834 -3.01 -0.91 11.7ms\n",
" 124 +4.656539691829 -3.18 -1.06 8.75ms\n",
" 125 +4.655718288245 -3.09 -1.19 11.8ms\n",
" 126 +4.655074618551 -3.19 -1.18 11.6ms\n",
" 127 +4.654475324300 -3.22 -1.17 8.58ms\n",
" 128 +4.653904395163 -3.24 -1.14 11.8ms\n",
" 129 +4.653181522739 -3.14 -1.13 8.66ms\n",
" 130 +4.652548595928 -3.20 -0.91 11.8ms\n",
" 131 +4.651798539700 -3.12 -0.90 11.8ms\n",
" 132 +4.650818410843 -3.01 -0.90 8.64ms\n",
" 133 +4.649985963347 -3.08 -0.96 11.8ms\n",
" 134 +4.649183807112 -3.10 -1.17 11.8ms\n",
" 135 +4.648380073304 -3.09 -1.18 8.78ms\n",
" 136 +4.647525884258 -3.07 -1.09 11.8ms\n",
" 137 +4.646816309371 -3.15 -1.08 8.69ms\n",
" 138 +4.646347574989 -3.33 -1.07 12.0ms\n",
" 139 +4.645883982502 -3.33 -1.15 11.7ms\n",
" 140 +4.645320775206 -3.25 -1.18 8.70ms\n",
" 141 +4.644922992984 -3.40 -1.28 11.9ms\n",
" 142 +4.644646376723 -3.56 -1.40 11.6ms\n",
" 143 +4.644327081774 -3.50 -1.32 8.67ms\n",
" 144 +4.643995855926 -3.48 -1.16 11.7ms\n",
" 145 +4.643660605706 -3.47 -1.19 8.52ms\n",
" 146 +4.643423233897 -3.62 -1.25 11.7ms\n",
" 147 +4.643160769994 -3.58 -1.39 11.6ms\n",
" 148 +4.642804953965 -3.45 -1.34 8.65ms\n",
" 149 +4.642562214683 -3.61 -1.47 11.8ms\n",
" 150 +4.642334627774 -3.64 -1.43 8.73ms\n",
" 151 +4.642131262001 -3.69 -1.34 12.0ms\n",
" 152 +4.641971796184 -3.80 -1.41 11.6ms\n",
" 153 +4.641823561638 -3.83 -1.33 8.63ms\n",
" 154 +4.641680379947 -3.84 -1.38 11.8ms\n",
" 155 +4.641564877971 -3.94 -1.50 11.8ms\n",
" 156 +4.641474820629 -4.05 -1.47 8.59ms\n",
" 157 +4.641390287007 -4.07 -1.56 11.8ms\n",
" 158 +4.641330561129 -4.22 -1.58 8.49ms\n",
" 159 +4.641263834241 -4.18 -1.61 11.8ms\n",
" 160 +4.641203411815 -4.22 -1.73 11.7ms\n",
" 161 +4.641162942194 -4.39 -1.84 8.60ms\n",
" 162 +4.641125533739 -4.43 -1.98 11.9ms\n",
" 163 +4.641096411580 -4.54 -1.97 11.6ms\n",
" 164 +4.641059231808 -4.43 -1.86 8.74ms\n",
" 165 +4.641036365711 -4.64 -1.86 11.9ms\n",
" 166 +4.641012712625 -4.63 -2.00 8.58ms\n",
" 167 +4.640989362761 -4.63 -2.11 11.8ms\n",
" 168 +4.640960472489 -4.54 -2.06 11.6ms\n",
" 169 +4.640941703346 -4.73 -2.02 8.79ms\n",
" 170 +4.640922063548 -4.71 -1.97 11.9ms\n",
" 171 +4.640900945749 -4.68 -1.95 11.9ms\n",
" 172 +4.640878312622 -4.65 -1.95 8.68ms\n",
" 173 +4.640849761811 -4.54 -1.94 11.7ms\n",
" 174 +4.640820488212 -4.53 -1.95 8.49ms\n",
" 175 +4.640796527453 -4.62 -1.83 11.7ms\n",
" 176 +4.640773749136 -4.64 -1.90 11.7ms\n",
" 177 +4.640755346773 -4.74 -1.85 8.70ms\n",
" 178 +4.640734824353 -4.69 -1.90 11.8ms\n",
" 179 +4.640720032238 -4.83 -2.00 11.4ms\n",
" 180 +4.640705276384 -4.83 -2.07 8.75ms\n",
" 181 +4.640693964022 -4.95 -2.07 11.9ms\n",
" 182 +4.640685989244 -5.10 -2.01 8.59ms\n",
" 183 +4.640678048050 -5.10 -2.10 11.7ms\n",
" 184 +4.640668246646 -5.01 -2.07 11.6ms\n",
" 185 +4.640660946961 -5.14 -2.10 8.57ms\n",
" 186 +4.640654574525 -5.20 -2.20 11.6ms\n",
" 187 +4.640647310593 -5.14 -2.29 8.59ms\n",
" 188 +4.640641768344 -5.26 -2.14 11.9ms\n",
" 189 +4.640635041669 -5.17 -2.06 11.7ms\n",
" 190 +4.640628757081 -5.20 -2.16 8.53ms\n",
" 191 +4.640620486203 -5.08 -2.05 11.7ms\n",
" 192 +4.640610543550 -5.00 -2.05 11.8ms\n",
" 193 +4.640601292369 -5.03 -1.99 8.67ms\n",
" 194 +4.640593807345 -5.13 -1.90 32.6ms\n",
" 195 +4.640584153370 -5.02 -1.89 8.69ms\n",
" 196 +4.640576025855 -5.09 -1.96 11.9ms\n",
" 197 +4.640567866610 -5.09 -2.01 11.7ms\n",
" 198 +4.640560856329 -5.15 -2.06 8.75ms\n",
" 199 +4.640553183725 -5.12 -2.08 11.8ms\n",
" 200 +4.640546837934 -5.20 -1.99 11.7ms\n",
" 201 +4.640541665762 -5.29 -2.01 8.70ms\n",
" 202 +4.640535835510 -5.23 -2.15 11.7ms\n",
" 203 +4.640530783046 -5.30 -2.19 8.56ms\n",
" 204 +4.640526287877 -5.35 -2.23 11.8ms\n",
" 205 +4.640522778315 -5.45 -2.25 11.8ms\n",
" 206 +4.640520184378 -5.59 -2.33 8.62ms\n",
" 207 +4.640518039249 -5.67 -2.31 11.8ms\n",
" 208 +4.640515350266 -5.57 -2.41 11.6ms\n",
" 209 +4.640513025613 -5.63 -2.49 8.69ms\n",
" 210 +4.640511199883 -5.74 -2.47 11.9ms\n",
" 211 +4.640508984829 -5.65 -2.48 8.58ms\n",
" 212 +4.640507044400 -5.71 -2.47 12.0ms\n",
" 213 +4.640505353849 -5.77 -2.40 11.6ms\n",
" 214 +4.640503174248 -5.66 -2.46 8.67ms\n",
" 215 +4.640500803781 -5.63 -2.49 11.8ms\n",
" 216 +4.640498708346 -5.68 -2.46 8.54ms\n",
" 217 +4.640496745789 -5.71 -2.42 12.0ms\n",
" 218 +4.640494839801 -5.72 -2.40 11.8ms\n",
" 219 +4.640493113532 -5.76 -2.31 8.56ms\n",
" 220 +4.640491301012 -5.74 -2.40 11.9ms\n",
" 221 +4.640489842272 -5.84 -2.50 11.7ms\n",
" 222 +4.640488641514 -5.92 -2.55 8.64ms\n",
" 223 +4.640487716055 -6.03 -2.69 11.9ms\n",
" 224 +4.640487076062 -6.19 -2.63 8.57ms\n",
" 225 +4.640486542766 -6.27 -2.74 11.8ms\n",
" 226 +4.640486152829 -6.41 -2.79 11.7ms\n",
" 227 +4.640485706201 -6.35 -2.94 8.53ms\n",
" 228 +4.640485378963 -6.49 -3.00 12.0ms\n",
" 229 +4.640485102995 -6.56 -3.03 11.9ms\n",
" 230 +4.640484874210 -6.64 -2.96 8.79ms\n",
" 231 +4.640484639727 -6.63 -2.98 11.8ms\n",
" 232 +4.640484384228 -6.59 -2.96 8.51ms\n",
" 233 +4.640484098832 -6.54 -2.95 11.9ms\n",
" 234 +4.640483766620 -6.48 -2.98 11.8ms\n",
" 235 +4.640483451967 -6.50 -2.95 8.64ms\n",
" 236 +4.640483155727 -6.53 -2.78 11.7ms\n",
" 237 +4.640482872362 -6.55 -2.79 11.7ms\n",
" 238 +4.640482544118 -6.48 -2.78 8.64ms\n",
" 239 +4.640482176640 -6.43 -2.81 11.9ms\n",
" 240 +4.640481831183 -6.46 -2.83 8.56ms\n",
" 241 +4.640481462143 -6.43 -2.81 11.8ms\n",
" 242 +4.640481195534 -6.57 -2.83 11.6ms\n",
" 243 +4.640480934298 -6.58 -2.75 8.79ms\n",
" 244 +4.640480638412 -6.53 -2.78 11.9ms\n",
" 245 +4.640480439309 -6.70 -2.91 11.7ms\n",
" 246 +4.640480234806 -6.69 -2.88 8.69ms\n",
" 247 +4.640480073269 -6.79 -2.99 11.8ms\n",
" 248 +4.640479942719 -6.88 -3.02 8.53ms\n",
" 249 +4.640479855452 -7.06 -2.96 11.8ms\n",
" 250 +4.640479745736 -6.96 -3.08 11.7ms\n",
" 251 +4.640479650558 -7.02 -3.10 8.65ms\n",
" 252 +4.640479558344 -7.04 -3.11 11.8ms\n",
" 253 +4.640479457582 -7.00 -3.15 8.62ms\n",
" 254 +4.640479350209 -6.97 -3.07 12.1ms\n",
" 255 +4.640479257560 -7.03 -2.92 12.0ms\n",
" 256 +4.640479118823 -6.86 -2.94 8.58ms\n",
" 257 +4.640478986126 -6.88 -2.89 12.0ms\n",
" 258 +4.640478823391 -6.79 -2.89 11.8ms\n",
" 259 +4.640478664329 -6.80 -2.81 8.99ms\n",
" 260 +4.640478523651 -6.85 -2.81 11.8ms\n",
" 261 +4.640478402063 -6.92 -2.85 8.50ms\n",
" 262 +4.640478286020 -6.94 -2.77 11.9ms\n",
" 263 +4.640478162543 -6.91 -3.00 11.7ms\n",
" 264 +4.640478066594 -7.02 -3.04 8.65ms\n",
" 265 +4.640477977485 -7.05 -3.07 11.9ms\n",
" 266 +4.640477921523 -7.25 -3.13 11.8ms\n",
" 267 +4.640477872842 -7.31 -3.23 8.65ms\n",
" 268 +4.640477836013 -7.43 -3.25 11.7ms\n",
" 269 +4.640477798360 -7.42 -3.45 8.54ms\n",
" 270 +4.640477769127 -7.53 -3.60 11.7ms\n",
" 271 +4.640477744929 -7.62 -3.50 11.6ms\n",
" 272 +4.640477723655 -7.67 -3.58 8.57ms\n",
" 273 +4.640477705576 -7.74 -3.55 11.7ms\n",
" 274 +4.640477683623 -7.66 -3.43 11.6ms\n",
" 275 +4.640477663889 -7.70 -3.54 8.66ms\n",
" 276 +4.640477644288 -7.71 -3.59 11.9ms\n",
" 277 +4.640477623690 -7.69 -3.53 8.56ms\n",
" 278 +4.640477608209 -7.81 -3.54 11.9ms\n",
" 279 +4.640477590737 -7.76 -3.41 11.7ms\n",
" 280 +4.640477574881 -7.80 -3.43 8.71ms\n",
" 281 +4.640477556835 -7.74 -3.47 11.8ms\n",
" 282 +4.640477538253 -7.73 -3.47 11.8ms\n",
" 283 +4.640477520027 -7.74 -3.53 8.71ms\n",
" 284 +4.640477506438 -7.87 -3.53 11.9ms\n",
" 285 +4.640477494334 -7.92 -3.48 8.53ms\n",
" 286 +4.640477483386 -7.96 -3.55 11.9ms\n",
" 287 +4.640477473697 -8.01 -3.61 11.8ms\n",
" 288 +4.640477463703 -8.00 -3.65 8.73ms\n",
" 289 +4.640477456292 -8.13 -3.83 11.9ms\n",
" 290 +4.640477450260 -8.22 -3.76 9.05ms\n",
" 291 +4.640477445832 -8.35 -3.74 29.4ms\n",
" 292 +4.640477441374 -8.35 -3.82 12.5ms\n",
" 293 +4.640477437358 -8.40 -3.88 8.62ms\n",
" 294 +4.640477433769 -8.44 -3.95 11.9ms\n",
" 295 +4.640477430538 -8.49 -4.02 12.0ms\n",
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" 483 +4.640477343383 -13.91 -6.64 8.68ms\n",
" 484 +4.640477343383 + -Inf -6.61 29.5ms\n",
" 485 +4.640477343383 -13.85 -6.66 8.66ms\n",
" 486 +4.640477343383 -13.80 -6.44 12.0ms\n",
" 487 +4.640477343383 -14.75 -6.60 11.6ms\n",
" 488 +4.640477343383 -13.85 -6.67 8.49ms\n",
" 489 +4.640477343383 -14.35 -6.75 15.5ms\n",
" 490 +4.640477343383 -15.05 -6.73 16.2ms\n",
" 491 +4.640477343383 -15.05 -6.68 9.85ms\n",
" 492 +4.640477343383 -14.21 -6.49 8.67ms\n",
" 493 +4.640477343383 -14.45 -6.46 11.7ms\n",
" 494 +4.640477343383 -13.80 -6.41 8.60ms\n",
" 495 +4.640477343383 -14.35 -6.49 11.8ms\n",
" 496 +4.640477343383 -14.10 -6.60 11.7ms\n",
" 497 +4.640477343383 + -Inf -6.66 6.65ms\n",
" 498 +4.640477343383 -13.97 -6.74 11.6ms\n",
" 499 +4.640477343383 -13.67 -6.74 8.60ms\n",
" 500 +4.640477343383 -14.75 -6.48 11.6ms\n",
" 501 +4.640477343383 -13.91 -6.73 11.7ms\n",
" 502 +4.640477343383 -14.15 -6.43 8.58ms\n",
" 503 +4.640477343383 -13.91 -6.56 11.5ms\n",
" 504 +4.640477343383 -15.05 -7.02 11.8ms\n",
" 505 +4.640477343383 -14.35 -6.96 8.72ms\n",
" 506 +4.640477343383 -14.15 -7.12 11.7ms\n",
"┌ Warning: DM not converged.\n",
"└ @ DFTK ~/work/DFTK.jl/DFTK.jl/src/scf/scf_callbacks.jl:60\n",
"e(1,1) / (2π) = 1.2112891860627029\n"
]
},
{
"output_type": "execute_result",
"data": {
"text/plain": "Plot{Plots.GRBackend() n=1}",
"image/png": 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},
"metadata": {},
"execution_count": 1
}
],
"cell_type": "code",
"source": [
"using DFTK\n",
"using StaticArrays\n",
"using Plots\n",
"\n",
"# Unit cell. Having one of the lattice vectors as zero means a 2D system\n",
"a = 14\n",
"lattice = a .* [[1 0 0.]; [0 1 0]; [0 0 0]];\n",
"\n",
"# Confining scalar potential\n",
"pot(x, y, z) = ((x - a/2)^2 + (y - a/2)^2);\n",
"\n",
"# Parameters\n",
"Ecut = 50\n",
"n_electrons = 1\n",
"β = 5;\n",
"\n",
"# Collect all the terms, build and run the model\n",
"terms = [Kinetic(; scaling_factor=2),\n",
" ExternalFromReal(X -> pot(X...)),\n",
" Anyonic(1, β)\n",
"]\n",
"model = Model(lattice; n_electrons, terms, spin_polarization=:spinless) # \"spinless electrons\"\n",
"basis = PlaneWaveBasis(model; Ecut, kgrid=(1, 1, 1))\n",
"scfres = direct_minimization(basis, tol=1e-14) # Reduce tol for production\n",
"E = scfres.energies.total\n",
"s = 2\n",
"E11 = π/2 * (2(s+1)/s)^((s+2)/s) * (s/(s+2))^(2(s+1)/s) * E^((s+2)/s) / β\n",
"println(\"e(1,1) / (2π) = \", E11 / (2π))\n",
"heatmap(scfres.ρ[:, :, 1, 1], c=:blues)"
],
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"execution_count": 1
}
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