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fixed greens function at finite temperature??
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@Anjishnubose
Anjishnubose committed Mar 19, 2024
1 parent f823bfd commit e547ed9
Showing 1 changed file with 33 additions and 20 deletions.
53 changes: 33 additions & 20 deletions src/BdGModel.jl
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Original file line number Diff line number Diff line change
Expand Up @@ -6,7 +6,7 @@ module BdG
using ..TightBindingToolkit.DesignUCell: ModifyIsotropicFields!
using ..TightBindingToolkit.BZone:BZ, MomentumPhaseFFT
using ..TightBindingToolkit.Hams:Hamiltonian, ModifyHamiltonianField!

using LinearAlgebra, Tullio, TensorCast, Logging, Statistics

import ..TightBindingToolkit.TBModel:FindFilling, GetMu!, GetFilling!, GetGk!, GetGr!, SolveModel!, GetGap!, FreeEnergy
Expand All @@ -27,7 +27,7 @@ module BdG
- `Gk :: Array{Matrix{ComplexF64}}` : An Array (corresponding to the grid of k-points in `BZ`) of Greens functions.
- `Fk :: Array{Matrix{ComplexF64}}` : An Array (corresponding to the grid of k-points in `BZ`) of anomalous Greens functions.
Initialize this structure using
Initialize this structure using
```julia
BdGModel(uc_hop::UnitCell, uc_pair::UnitCell, bz::BZ, Ham::Hamiltonian ; T::Float64=1e-3, filling::Float64=-1.0, mu::Float64=0.0, stat::Int64=-1)
```
Expand All @@ -53,7 +53,7 @@ module BdG
Fk :: Array{Matrix{ComplexF64}}
Gr :: Array{Matrix{ComplexF64}}
Fr :: Array{Matrix{ComplexF64}}

BdGModel(uc_hop::UnitCell, uc_pair::UnitCell, bz::BZ, Ham::Hamiltonian ; T::Float64=1e-3, filling::Float64=-1.0, mu::Float64=0.0, stat::Int64=-1) = new{}(uc_hop, uc_pair, bz, Ham, T, filling, mu, -999.0, stat ,Array{Matrix{ComplexF64}}(undef, zeros(Int64, length(uc_hop.primitives))...), Array{Matrix{ComplexF64}}(undef, zeros(Int64, length(uc_hop.primitives))...), Array{Matrix{ComplexF64}}(undef, zeros(Int64, length(uc_hop.primitives))...),Array{Matrix{ComplexF64}}(undef, zeros(Int64, length(uc_hop.primitives))...))
##### Chosen the default value of filling to be -1 which is unphysical so that the code knows when filling has not been provided and has to be calculated from mu instead!
end
Expand All @@ -75,10 +75,12 @@ Because of this, if you want to calculate the filling at a different chemical po
Eks = reshape(getindex.(M.Ham.bands, Ref(1:N÷2)), prod(M.bz.gridSize))
U11s = reshape(getindex.(M.Ham.states, Ref(1:N÷2), Ref(1:N÷2)), prod(M.bz.gridSize))
U21s = reshape(getindex.(M.Ham.states, Ref(N÷2 + 1: N), Ref(1:N÷2)), prod(M.bz.gridSize))
U12s = reshape(getindex.(M.Ham.states, Ref(1:N÷2), Ref(N÷2 + 1: N)) , prod(M.bz.gridSize))
U22s = reshape(getindex.(M.Ham.states, Ref(N÷2 + 1: N), Ref(N÷2 + 1: N)) , prod(M.bz.gridSize))

nFs = DistFunction.(Eks; T=M.T, mu=0.0, stat=M.stat)

@tullio filling := ((conj(U11s[k1][i, j]) * U11s[k1][i, j] * nFs[k1][j])
@tullio filling := ((conj(U11s[k1][i, j]) * U11s[k1][i, j] * nFs[k1][j])
+ (conj(U21s[k1][i, j]) * U21s[k1][i, j] * (1 - nFs[k1][j])))

return real(filling) / (prod(M.bz.gridSize) * M.uc_hop.localDim * length(M.uc_hop.basis))
Expand Down Expand Up @@ -109,9 +111,9 @@ GetMu!(M::BdGModel ; tol::Float64=0.001)
Function to get the correct chemical potential given a filling.
"""
function GetMu!(M::BdGModel ; guess::Float64 = 0.0, mu_tol::Float64 = 0.001, filling_tol::Float64 = 1e-6)
M.mu = BinarySearch(M.filling, M.Ham.bandwidth, FindFilling, (M,) ; initial = guess, x_tol = mu_tol, target_tol = filling_tol)
M.mu = BinarySearch(M.filling, (2*M.Ham.bandwidth[1], 2*M.Ham.bandwidth[2]), FindFilling, (M,) ; initial = guess, x_tol = mu_tol, target_tol = filling_tol)
@info "Found chemical potential μ = $(M.mu) for given filling = $(M.filling)."

end


Expand All @@ -127,16 +129,16 @@ Finding the Greens functions, and anomalous greens functions in momentum space a
Eks = reshape(getindex.(M.Ham.bands, Ref(1:N÷2)) , prod(M.bz.gridSize)) ##### Only the negative energies from the bdG spectrum

U11s = reshape(getindex.(M.Ham.states, Ref(1:N÷2), Ref(1:N÷2)) , prod(M.bz.gridSize)) ##### The 4 different quadrants in the Unitary relating the BdG quasiparticles and the nambu basis
U21s = reshape(getindex.(M.Ham.states, Ref(N÷2 + 1: N), Ref(1:N÷2)) , prod(M.bz.gridSize))
U12s = reshape(getindex.(M.Ham.states, Ref(1:N÷2), Ref(N÷2 + 1: N)) , prod(M.bz.gridSize))
U21s = reshape(getindex.(M.Ham.states, Ref(N÷2 + 1: N), Ref(1:N÷2)) , prod(M.bz.gridSize))
U12s = reshape(getindex.(M.Ham.states, Ref(1:N÷2), Ref(N÷2 + 1: N)) , prod(M.bz.gridSize))
U22s = reshape(getindex.(M.Ham.states, Ref(N÷2 + 1: N), Ref(N÷2 + 1: N)) , prod(M.bz.gridSize))

nFs = DistFunction.(Eks; T=M.T, mu=0.0, stat=M.stat)

@reduce Gk[k1][i, j] |= sum(l) ((conj(U11s[k1][i, l]) * U11s[k1][j, l] * nFs[k1][l])
+ (conj(U12s[k1][i, l]) * U12s[k1][j, l] * (1 - nFs[k1][l])))
@reduce Gk[k1][i, j] |= sum(l) ((conj(U11s[k1][i, l]) * U11s[k1][j, l] * nFs[k1][l])
+ (conj(U21s[k1][i, l]) * U21s[k1][j, l] * (1 - nFs[k1][l])))

@reduce Fk[k1][i, j] |= sum(l) ((conj(U11s[k1][i, l]) * U21s[k1][j, l] * nFs[k1][l])
@reduce Fk[k1][i, j] |= sum(l) ((conj(U11s[k1][i, l]) * U21s[k1][j, l] * nFs[k1][l])
+ (conj(U12s[k1][i, l]) * U22s[k1][j, l] * (1 - nFs[k1][l])))
M.Gk = reshape(Gk, M.bz.gridSize...)
M.Fk = reshape(Fk, M.bz.gridSize...)
Expand All @@ -152,14 +154,14 @@ Finding the equal-time Greens functions and anomalous Greens function in real sp
"""
function GetGr!(M::BdGModel)

phaseShift = MomentumPhaseFFT(M.bz, M.uc_hop)

Gr = FFTArrayofMatrix(M.Gk)
M.Gr = Gr .* phaseShift
Gr = FFTArrayofMatrix(M.Gk)
M.Gr = Gr .* phaseShift

Fr = FFTArrayofMatrix(M.Fk)
M.Fr = Fr .* phaseShift
Fr = FFTArrayofMatrix(M.Fk)
M.Fr = Fr .* phaseShift
end


Expand All @@ -169,9 +171,10 @@ SolveModel!(M::BdGModel)
```
one-step function to find all the attributes in BdGModel after it has been initialized.
"""
function SolveModel!(M::BdGModel ; mu_guess::Float64 = M.Ham.bandwidth[1] + M.filling * (M.Ham.bandwidth[2] - M.Ham.bandwidth[1]), get_correlations::Bool = true, get_gap::Bool = false, verbose::Bool = true, mu_tol::Float64 = 1e-3, filling_tol::Float64 = 1e-6)
function SolveModel!(M::BdGModel ; mu_guess::Float64 = 2*M.Ham.bandwidth[1] + 2*M.filling * (M.Ham.bandwidth[2] - M.Ham.bandwidth[1]), get_correlations::Bool = true, get_gap::Bool = false, verbose::Bool = true, mu_tol::Float64 = 1e-3, filling_tol::Float64 = 1e-6)
@assert M.Ham.is_BdG==true "Use other format for pure hopping Hamiltonian"

# println(mu_guess)
# println(M.Ham.bandwidth)
if M.filling<0 ##### Must imply that filling was not provided by user and hence needs to be calculated from given mu
GetFilling!(M)
else
Expand All @@ -188,7 +191,7 @@ one-step function to find all the attributes in BdGModel after it has been init
GetGk!(M)
GetGr!(M)
end

if verbose
@info "System Filled!"
end
Expand Down Expand Up @@ -225,4 +228,14 @@ Calculate the free energy of the given `BdGModel`.
end


end
# function entropy(M::BdGModel)
# Es = 2*reduce(vcat, M.Ham.bands)
# ps = DistFunction(Es; T=M.T, mu=M.mu, stat=M.stat)


# return S


end

# end

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