MaximallyLocalizedWannierFunctions

Hamiltonian{T<:Real, V<:AbstractVector{T}} <: Function

The Hamiltonian function based on Wannier interpolation.

MLWF(tba::TBA, brillouinzone::BrillouinZone, bands::AbstractVector{Int}, guess::Union{δ, Nothing}=nothing; kwargs...)
MLWF(hamiltonian::Function, lattice::Lattice, brillouinzone::BrillouinZone, bands::AbstractVector{Int}, guess::Union{δ, Nothing}=nothing; kwargs...)

Initialize a set of maximally localized Wannier functions.

MLWF{L<:Lattice, B<:BrillouinZone, T<:Real, V<:AbstractVector{T}} <: Function

Maximally localized Wannier functions on a Monkhorst-Pack mesh.

(mlwf::MLWF)(coordinate::AbstractVector) -> Matrix{Complex{dtype(mlwf)}}

Get the values of the wannier functions at each lattice point.

δ{T<:Real} <: Function

Delta function like Wannier functions.

finitedifferences(vectors::AbstractVector{<:AbstractVector}; nneighbor::Int=12, coordination::Int=12) -> Tuple{Vector, Vector{Vector}}

Get the weights and difference vectors of a Monkhorst-Pack discretization scheme whose minimum mesh translations are given by vectors.

See Sec. 3.2 in Reference for the details of the method.

gradient(mlwf::MLWF) -> Vector{Matrix{Complex{dtype(mlwf)}}}

The gradient of the spread functional of the Wannier functions with respect to the infinitesimal gauge transformations at each momentum point.

r²ₙ(mlwf::MLWF) -> Vector{dtype(mlwf)}

⟨r²ₙ⟩, i.e., the expectation value of r²ₙ for each Wannier function.

rₙ(mlwf::MLWF) -> Vector{Vector{dtype(mlwf)}}

⟨rₙ⟩, i.e. the centers of the Wannier functions.

Ω(mlwf::MLWF) -> dtype(mlwf)

The value of the spread functional of the Wannier functions.

Ω₁(mlwf::MLWF) -> dtype(mlwf)

The gauge-invariant part of the spread functional of the Wannier functions.

Ω₂(mlwf::MLWF) -> dtype(mlwf)

The gauge-dependent part of the spread functional of the Wannier functions.

update!(mlwf::MLWF, ::GradientDescent) -> MLWF

Update the maximally localized Wannier functions by the gradient descent method.

optimize!(mlwf::MLWF, method::FirstOrderOptimizer=GradientDescent(); maxiter::Int=20000, atol=atol, rtol=rtol, verbose::Union{Nothing, Int}=nothing) -> MLWF

Optimize a set of Wannier function to minimize the spread functional.