Reference

CubicLattice(L::Int)

CubicLattice with PBC boundary

3D Anderson-Hubbard Model. Hamiltonian see index part.

HubbardPara

• t : hopping amplitude
• U : Hubbard interaction
• W : disorder strength, onsite disorder energies are drawn from a Gaussian distribution in the interval [-W/2, W/2]
• n_up : ⟨n_{i↑}⟩ = ∑_{α} |⟨i↑|α⟩|^2
• n_down : ⟨n_{i↓}⟩ = ∑_{α} |⟨i↓|α ⟩|^2 [1]
• S_up : ⟨S_{i}^+⟩ = ∑_{α} |⟨0|c_{i↓}^† c_{i↑}⟩|α⟩|^2
• S_down : conjugation of S_up

[1] F.Fazileh et al. 2006 Physical Review Letters

checkConverge(data::SCFdata, n_up::Vector{Float64}, n_down::Vector{Float64}, S_up::Vector{Complex{Float64}})

check if SCF converges. Ref: Inui and Littlewood (1991)

getNMean(U::AbstractMatrix)

calculate ⟨n_{i}⟩ = ∑_{α} |⟨i|α ⟩|^2 where i ∈ 1:2L, α ∈ 1:N. 1:L labels spin-up operators, L+1:2L labels spin-down operators.

return: nup, ndown

getSupMean(U::AbstractMatrix)

return: S_up

init(rng::AbstractRNG, lat::CubicLattice)
initialize SCF guess

step!(data::SCFdata, lat::CubicLattice, para::HubbardPara)
step on SCF, if converge, returns true.