We solve the almost-bosonic anyon model of https://arxiv.org/pdf/1901.10739.pdf
using DFTK
using StaticArrays
using Plots
# Unit cell. Having one of the lattice vectors as zero means a 2D system
a = 14
lattice = a .* [[1 0 0.]; [0 1 0]; [0 0 0]];
# Confining scalar potential
pot(x, y, z) = ((x - a/2)^2 + (y - a/2)^2);
# Parameters
Ecut = 50
n_electrons = 1
β = 5;
# Collect all the terms, build and run the model
terms = [Kinetic(; scaling_factor=2),
ExternalFromReal(X -> pot(X...)),
Anyonic(1, β)
]
model = Model(lattice; n_electrons, terms, spin_polarization=:spinless) # "spinless electrons"
basis = PlaneWaveBasis(model; Ecut, kgrid=(1, 1, 1))
scfres = direct_minimization(basis, tol=1e-14) # Reduce tol for production
E = scfres.energies.total
s = 2
E11 = π/2 * (2(s+1)/s)^((s+2)/s) * (s/(s+2))^(2(s+1)/s) * E^((s+2)/s) / β
println("e(1,1) / (2π)= ", E11 / (2π))
heatmap(scfres.ρ[:, :, 1, 1], c=:blues)
Iter Function value Gradient norm 0 8.200289e+01 1.454467e+01 * time: 0.005261898040771484 1 6.046576e+01 9.704580e+00 * time: 0.014676809310913086 2 5.600278e+01 1.342225e+01 * time: 0.036894798278808594 3 3.834285e+01 8.853759e+00 * time: 0.210892915725708 4 2.860652e+01 7.242686e+00 * time: 0.24387001991271973 5 2.110059e+01 5.436010e+00 * time: 0.2709629535675049 6 2.077883e+01 6.471797e+00 * time: 0.29473090171813965 7 9.501739e+00 2.286331e+00 * time: 0.3187689781188965 8 6.752361e+00 2.244869e+00 * time: 0.3413078784942627 9 6.242284e+00 1.328768e+00 * time: 0.3638739585876465 10 6.080685e+00 1.415595e+00 * time: 0.382282018661499 11 5.993464e+00 1.201395e+00 * time: 0.40092897415161133 12 5.910314e+00 8.377229e-01 * time: 0.41904592514038086 13 5.840276e+00 7.393215e-01 * time: 0.437175989151001 14 5.797101e+00 5.593923e-01 * time: 0.45578598976135254 15 5.773644e+00 6.088645e-01 * time: 0.5431559085845947 16 5.752314e+00 5.112412e-01 * time: 0.5610578060150146 17 5.737885e+00 1.144800e+00 * time: 0.5744550228118896 18 5.705868e+00 7.519057e-01 * time: 0.588249921798706 19 5.674153e+00 6.088696e-01 * time: 0.6020488739013672 20 5.638859e+00 6.919618e-01 * time: 0.615670919418335 21 5.618025e+00 3.521743e-01 * time: 0.6341109275817871 22 5.611260e+00 5.395682e-01 * time: 0.6476008892059326 23 5.598189e+00 4.058224e-01 * time: 0.665855884552002 24 5.587904e+00 4.003910e-01 * time: 0.6794819831848145 25 5.581449e+00 2.705804e-01 * time: 0.6933939456939697 26 5.579960e+00 3.429019e-01 * time: 0.7083039283752441 27 5.572904e+00 1.868303e-01 * time: 0.7227308750152588 28 5.571181e+00 1.895262e-01 * time: 0.741567850112915 29 5.567069e+00 2.424169e-01 * time: 0.7553949356079102 30 5.566763e+00 2.805680e-01 * time: 0.7692439556121826 31 5.566114e+00 1.559386e-01 * time: 0.7837178707122803 32 5.564883e+00 1.838331e-01 * time: 0.798846960067749 33 5.563777e+00 9.072058e-02 * time: 0.8781428337097168 34 5.563245e+00 1.158905e-01 * time: 0.8939008712768555 35 5.562361e+00 9.000053e-02 * time: 0.9076528549194336 36 5.561655e+00 6.989616e-02 * time: 0.9212779998779297 37 5.561441e+00 9.758331e-02 * time: 0.9347019195556641 38 5.561137e+00 6.924282e-02 * time: 0.949638843536377 39 5.561125e+00 8.751227e-02 * time: 0.9638168811798096 40 5.560963e+00 3.948629e-02 * time: 0.9818358421325684 41 5.560779e+00 5.584112e-02 * time: 0.9956657886505127 42 5.560700e+00 6.867982e-02 * time: 1.008971929550171 43 5.560636e+00 3.988749e-02 * time: 1.0221788883209229 44 5.560602e+00 3.007347e-02 * time: 1.0353589057922363 45 5.560597e+00 3.458839e-02 * time: 1.0494978427886963 46 5.560570e+00 1.872054e-02 * time: 1.0687198638916016 47 5.560548e+00 1.725754e-02 * time: 1.0878658294677734 48 5.560518e+00 1.617112e-02 * time: 1.1019480228424072 49 5.560514e+00 2.324838e-02 * time: 1.1154999732971191 50 5.560497e+00 1.218610e-02 * time: 1.1290688514709473 51 5.560486e+00 1.302545e-02 * time: 1.166562795639038 52 5.560483e+00 1.638541e-02 * time: 1.18241286277771 53 5.560479e+00 1.171836e-02 * time: 1.196631908416748 54 5.560473e+00 8.094007e-03 * time: 1.215466022491455 55 5.560470e+00 7.455271e-03 * time: 1.2339179515838623 56 5.560467e+00 5.691004e-03 * time: 1.2475829124450684 57 5.560466e+00 7.749086e-03 * time: 1.2617719173431396 58 5.560466e+00 6.431027e-03 * time: 1.2750539779663086 59 5.560465e+00 4.257302e-03 * time: 1.2938299179077148 60 5.560465e+00 4.525134e-03 * time: 1.3072218894958496 61 5.560464e+00 4.140827e-03 * time: 1.3203649520874023 62 5.560464e+00 2.903045e-03 * time: 1.3344128131866455 63 5.560464e+00 1.769375e-03 * time: 1.347625970840454 64 5.560464e+00 1.896148e-03 * time: 1.365858793258667 65 5.560463e+00 3.897075e-03 * time: 1.3795068264007568 66 5.560463e+00 1.941512e-03 * time: 1.3986079692840576 67 5.560463e+00 2.877500e-03 * time: 1.4125878810882568 68 5.560463e+00 1.746326e-03 * time: 1.427060842514038 69 5.560463e+00 1.291818e-03 * time: 1.4626379013061523 70 5.560463e+00 1.029335e-03 * time: 1.4769179821014404 71 5.560463e+00 9.204316e-04 * time: 1.4961438179016113 72 5.560463e+00 6.169948e-04 * time: 1.516507863998413 73 5.560463e+00 7.875155e-04 * time: 1.531303882598877 74 5.560463e+00 1.278484e-03 * time: 1.545435905456543 75 5.560463e+00 6.520756e-04 * time: 1.5588958263397217 76 5.560463e+00 8.250427e-04 * time: 1.5722320079803467 77 5.560463e+00 6.891213e-04 * time: 1.5858688354492188 78 5.560463e+00 5.768669e-04 * time: 1.5992839336395264 79 5.560463e+00 3.228600e-04 * time: 1.6176369190216064 80 5.560463e+00 3.575937e-04 * time: 1.631910800933838 81 5.560463e+00 5.129062e-04 * time: 1.6452419757843018 82 5.560463e+00 4.093644e-04 * time: 1.6590509414672852 83 5.560463e+00 9.684812e-04 * time: 1.6733458042144775 84 5.560463e+00 6.799935e-04 * time: 1.6877129077911377 85 5.560463e+00 4.643456e-04 * time: 1.7011868953704834 86 5.560463e+00 2.734082e-04 * time: 1.7144629955291748 87 5.560463e+00 6.052775e-04 * time: 1.7511019706726074 88 5.560463e+00 5.340380e-04 * time: 1.765038013458252 89 5.560463e+00 3.653612e-04 * time: 1.7833077907562256 90 5.560463e+00 3.061180e-04 * time: 1.7968418598175049 91 5.560463e+00 3.155435e-04 * time: 1.8107388019561768 92 5.560463e+00 2.386411e-04 * time: 1.829455852508545 93 5.560463e+00 1.996828e-04 * time: 1.8478968143463135 94 5.560463e+00 4.678266e-04 * time: 1.8678460121154785 95 5.560463e+00 4.255047e-04 * time: 1.8883638381958008 96 5.560463e+00 3.006264e-04 * time: 1.9024338722229004 97 5.560463e+00 2.568562e-04 * time: 1.9153308868408203 98 5.560463e+00 2.517784e-04 * time: 1.9367499351501465 99 5.560463e+00 1.650642e-04 * time: 1.9554708003997803 100 5.560463e+00 1.588244e-04 * time: 1.9688389301300049 101 5.560463e+00 7.881208e-05 * time: 1.986454963684082 102 5.560463e+00 6.136900e-05 * time: 2.0039868354797363 103 5.560463e+00 5.690330e-05 * time: 2.0254340171813965 104 5.560463e+00 5.690336e-05 * time: 2.0908617973327637 e(1,1) / (2π)= 1.7391793984948878