spectral functio response

Author: Anjishnubose

src/SpectralResponse.jl

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+module SpecResponse
+
+using LinearAlgebra
+
+using ..TightBindingToolkit.BZone: BZ, GetQIndex
+using ..TightBindingToolkit.Hams: Hamiltonian
+using ..TightBindingToolkit.Useful: DistFunction
+
+export spectral, response
+
+
+
+function spectral(omega::Float64, eta::Float64, ham::Hamiltonian)
+
+    G = Ref((omega+im*eta)*I) .- ham.H
+    G = inv.(G)
+
+    return (G - adjoint.(G)) / (2*im)
+end
+
+function spectral(eta::Float64, ham::Hamiltonian ; n_w::Int = 101)
+
+    omegas = collect(range(ham.bandwidth..., n_w))
+    return spectral.(omegas, eta, Ref(ham))
+end
+
+
+function response(omega::Float64, eta::Float64, QIndex::Vector{Int64}, Aws, bandwidth::Tuple{Float64, Float64} ;
+    n_w::Int = 101, mu::Float64 = 0.0, T::Float64 = 0.001)
+
+    es = collect(range(bandwidth..., n_w))
+    response = zeros(Complex{Float64}, size(Aws[1][1, 1]) .^ 2)
+    for (i1, e1) in enumerate(es)
+        for (i2, e2) in enumerate(es)
+            Ak1 = Aws[i1]
+            AQk2 = circshift(Aws[i2], -QIndex)
+            Aksum = sum(kron.(AQk2, Ak1))
+            nfs = (DistFunction(e1 ; T=T, mu=mu, stat=-1) - DistFunction(e2 ; T=T, mu=mu, stat=1))/(omega +im*eta + e1 - e2)
+            response += nfs * Aksum
+
+        end
+    end
+println("response done")
+    return response
+end
+
+
+function response(omegas::Vector{Float64}, eta::Float64, Qs::Vector{Vector{Float64}}, ham::Hamiltonian, bz::BZ ;
+    n_w::Int = 101, mu::Float64 = 0.0, T::Float64 = 0.001)
+
+    QIndices = GetQIndex.(Qs, Ref(bz)) .- Ref(GetQIndex(zeros(length(bz.basis)), bz))
+    Aws = spectral(eta, ham; n_w=n_w)
+    println("Aws done")
+    return response.(omegas', Ref(eta), QIndices, Ref(Aws), Ref(ham.bandwidth); n_w=n_w, mu=mu, T=T)
+end
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+end