gftool.siam.hamiltonian_matrix

gftool.siam.hamiltonian_matrix(e_onsite, e_bath, hopping)

One-particle Hamiltonian matrix of the SIAM.

The non-interacting Hamiltonian can be written in the form

\[\hat{H} = ∑_{ijσ} c^†_{iσ} H_{ijσ} c_{jσ}.\]

The Hamiltonian matrix is \(H_{ij}\), where we fixed the spin σ. The element H_{00} corresponds to the impurity site.

Parameters:

e_onsite(…) float np.ndarray

On-site energy of the impurity site.

e_bath(…, Nb) float np.ndarray

On-site energy of the bath sites.

hopping(…, Nb) complex np.ndarray

Hopping matrix element between impurity and the bath sites.

Returns:

(…, Nb+1, Nb+1) complex np.ndarray

Lesser Green’s function of the impurity site.