[Wannier] Downfolding and transfer integrals

[Oier Arcelus]

Hello Forum,

I want to calculate the magnetic exchange parameters of some very small clusters that I have relaxed. So I targeted my low energy bands of interests and extracted the MLWF out of them. I have the following questions.

1- If I express my GGA-type hamiltonian in the basis of my target wannier orbitals (If im not wrong, wannier90 already has a tag to do this) do the off diagonal elements express the values for the transfer integrals between my wannier functions?

2- To extract the J magnetic exchange interactions, do I need to apply the downfolding procedure to the subspace of pairs of wannier functions, so I can extract the effective hamiltonian that regards only to that pairs? If so, there is something that confuses me. As far as I understand, the downfolding procedure works to separate the high-energy degrees of freedom from the low-energy ones in which we are interested. However I only targeted low-energy bands so there are no high-energy degrees of freedom to be separated. Maybe I'm just writing non-sense I am not familiar with those concepts at all.

Cheers,

Oier.
 		 	   		  
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