gftool.matrix.gf_2x2_z

gftool.matrix.gf_2x2_z(z, eps0, eps1, hopping, hilbert_trafo=None)

Calculate the diagonal Green’s function elements for a 2x2 system.

Parameters:

z(…) complex array_like

Complex frequencies.

eps0, eps1(…) float or complex array_like

On-site energy of element 0 and 1. For interacting systems this can be replaced by on-site energy + self-energy.

hopping(…) float or complex array_like

Hopping element between element 0 and 1.

hilbert_trafoCallable, optional

Hilbert transformation. If given, return the local Green’s function. Else the lattice dispersion \(ϵ_k\) can be given via z → z - ϵ_k.

Returns:

(…, 2) complex array_like

Diagonal elements of the Green’s function of the 2x2 system.

Notes

For the trivial case eps0==eps1 and hopping==0, this implementation fails.