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)
n Energy log10(ΔE) log10(Δρ) Δtime --- --------------- --------- --------- ------ 1 +64.36949742807 -2.49 6.13s 2 +58.27460242935 0.78 -1.39 72.7ms 3 +42.75547208388 1.19 -1.01 14.3ms 4 +32.72182473424 1.00 -0.87 40.0ms 5 +28.65270254117 0.61 -0.76 12.3ms 6 +13.62042284706 1.18 -0.71 16.1ms 7 +12.88111147864 -0.13 -0.91 8.53ms 8 +10.92717077925 0.29 -0.63 14.1ms 9 +9.334307576085 0.20 -0.67 13.8ms 10 +7.680212136437 0.22 -0.73 13.8ms 11 +6.919436428620 -0.12 -0.66 8.65ms 12 +6.389827978826 -0.28 -0.68 12.0ms 13 +6.207808846761 -0.74 -0.76 11.9ms 14 +6.090523098309 -0.93 -0.77 8.83ms 15 +5.954415594367 -0.87 -0.83 12.0ms 16 +5.944013546273 -1.98 -0.88 6.68ms 17 +5.892941365545 -1.29 -0.90 9.89ms 18 +5.826726255386 -1.18 -0.95 6.83ms 19 +5.745943672255 -1.09 -0.99 9.91ms 20 +5.707653718832 -1.42 -1.01 8.54ms 21 +5.659841885200 -1.32 -0.85 11.8ms 22 +5.632943051951 -1.57 -1.00 11.7ms 23 +5.607223982781 -1.59 -1.25 6.80ms 24 +5.595945709876 -1.95 -1.22 11.8ms 25 +5.588827308814 -2.15 -1.27 8.57ms 26 +5.580525271263 -2.08 -1.36 11.8ms 27 +5.571857154876 -2.06 -1.50 6.70ms 28 +5.568465971100 -2.47 -1.24 9.93ms 29 +5.567657317603 -3.09 -1.57 6.63ms 30 +5.565756121210 -2.72 -1.82 9.79ms 31 +5.565038182986 -3.14 -1.81 6.63ms 32 +5.563665466976 -2.86 -1.60 11.8ms 33 +5.562528860565 -2.94 -1.72 11.8ms 34 +5.560377725829 -2.67 -1.76 6.83ms 35 +5.559276863161 -2.96 -1.70 11.8ms 36 +5.558900469181 -3.42 -1.86 6.72ms 37 +5.558524933287 -3.43 -1.85 11.8ms 38 +5.557951739196 -3.24 -1.72 6.66ms 39 +5.557832976259 -3.93 -1.82 9.92ms 40 +5.556855126483 -3.01 -1.83 6.73ms 41 +5.555854816213 -3.00 -1.63 9.84ms 42 +5.554582532236 -2.90 -1.19 6.69ms 43 +5.549979991108 -2.34 -1.34 9.92ms 44 +5.549594975354 -3.41 -0.83 6.75ms 45 +5.547443001357 -2.67 -0.74 9.78ms 46 +5.537982479542 -2.02 -0.68 8.64ms 47 +5.528001898549 -2.00 -0.68 12.0ms 48 +5.500301552405 -1.56 -0.58 8.74ms 49 +5.480504836116 -1.70 -0.64 12.0ms 50 +5.462094303668 -1.73 -0.67 11.8ms 51 +5.433076189719 -1.54 -0.78 8.52ms 52 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~/work/DFTK.jl/DFTK.jl/src/scf/scf_callbacks.jl:60 e(1,1) / (2π) = 1.2112891860627029