I am not sure whether we can implement a multi-orbital model with its specified interaction in current version of package. For example, given orbital A at a particular lattice position, it has its own μ_A, t_AA for same-orbital hopping, t_AB for different-orbital hopping, and U_A for Hubbard interaction. It is easy to implement the hopping matrix, but I am unsure about the interaction if I have more than one orbital {A, B, C}.
Due to a lack of documentation, it is difficult to figure out whether this feature is already part of the package or not. However, from what I can tell by reading the source code, it seems that this feature is not yet implemented and only supports Hubbard interaction for a single orbital. It does not require a lot of modification though. I only need to define my own interaction_matrix_exp and propose_local for different orbitals.
So, I need to construct the U matrix, specifically, the α.
then finally, the interaction term need to be written to be like this
@inline function interaction_matrix_exp!(f::MagneticHirschField, result::Diagonal, slice, power)
N = size(f.conf, 1)
@inbounds for i in axes(f.conf, 1)
result.diag[i] = exp( power * α[i] * f.conf[i, slice])
end
@inbounds for i in axes(f.conf, 1)
result.diag[i+N] = exp(-power * α[i] * f.conf[i, slice])
end
nothing
end
function propose_local(mc, f::MagneticHirschField, i, slice)
ΔE_Boson = -2.0 * α[i] * f.conf[i, slice]
mc.stack.field_cache.Δ[1] = exp(+ΔE_Boson) - 1.0
mc.stack.field_cache.Δ[2] = exp(-ΔE_Boson) - 1.0
detratio = calculate_detratio!(mc.stack.field_cache, mc.stack.greens, i)
# There is no bosonic part (exp(-ΔE_Boson)) to the partition function.
# Therefore pass 0.0
return detratio, 0.0, nothing
end
I am not sure whether we can implement a multi-orbital model with its specified interaction in current version of package. For example, given orbital A at a particular lattice position, it has its own
μ_A
,t_AA
for same-orbital hopping,t_AB
for different-orbital hopping, andU_A
for Hubbard interaction. It is easy to implement the hopping matrix, but I am unsure about the interaction if I have more than one orbital {A, B, C}.Due to a lack of documentation, it is difficult to figure out whether this feature is already part of the package or not. However, from what I can tell by reading the source code, it seems that this feature is not yet implemented and only supports Hubbard interaction for a single orbital. It does not require a lot of modification though. I only need to define my own
interaction_matrix_exp
andpropose_local
for different orbitals.So, I need to construct the
U
matrix, specifically, theα
.α[i] = acosh(exp(-0.5 * param.delta_tau * ComplexF64(U[i])))
where i is positions of sites.
then finally, the interaction term need to be written to be like this
let me know if this is correct approach.