gftool.cpa.self_root_eq

gftool.cpa.self_root_eq(self_cpa_z, z, e_onsite, concentration, hilbert_trafo: Callable[[complex], complex])

Root equation r(Σ)=0 for CPA.

The root equation writes r(Σ, z) = T(z) / (1 + T(z)*hilbert_trafo(z-Σ)).

Parameters

self_cpa_z(…) complex np.ndarray

CPA self-energy.

z(…) complex array_like

Frequency points.

e_onsite(…, N_cmpt) float or complex np.ndarray

On-site energy of the components. This can also include a local frequency dependent self-energy of the component sites.

concentration(…, N_cmpt) float array_like

Concentration of the different components used for the average.

hilbert_trafoCallable[[complex], complex]

Hilbert transformation of the lattice to calculate the coherent Green’s function.

Returns

remainder(…) complex np.ndarray

The result of r(Σ), if it is 0 and hence a root, self_cpa_z is the correct CPA self-energy.