Anyonic models

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)