gftool.siam

Basic functions for the (non-interacting) single impurity Anderson model (SIAM).

The Hamiltonian for the SIAM reads

\[H = ∑_σ ϵ_σ c^†_σ c_σ + U n_↓ n_↑ + ∑_{kσ} (V_{kσ} c^†_σ c_{kσ} + H.c.) + ∑_{kσ} ϵ_{kσ} n_{kσ}\]

The first to terms describe the interacting single impurity, the thirds term is the hopping (or hybridization) between impurity and bath-sites, the last term is the on-site energy of the non-interacting bath sites.

In the action formalism, the bath degrees of freedom can be readily integrated out, as the action is quadratic in these degrees. The local action of the impurity reads

\[S_{imp}[c^+_σ, c_σ] = -∑_{nσ} c^+_σ [iω_n - ϵ_σ - Δ(iω_n)] c_σ + U ∫_0^β dτ n_↑(τ) n_↓(τ)\]

with the hybridization function

\[Δ_σ(z) = ∑_{kσ} |V_{kσ}|^2 / (z - ϵ_{kσ}).\]

API

Functions

gf0_loc_gr_t(tt, e_onsite, e_bath, hopping, beta)	Noninteracting greater local Green’s function for the impurity.
gf0_loc_le_t(tt, e_onsite, e_bath, hopping, beta)	Noninteracting lesser local Green’s function for the impurity.
gf0_loc_ret_t(tt, e_onsite, e_bath, hopping)	Noninteracting retarded local Green’s function for the impurity.
gf0_loc_z(z, e_onsite, e_bath, hopping_sqr)	Noninteracting local Green’s function for the impurity.
hamiltonian_matrix(e_onsite, e_bath, hopping)	One-particle Hamiltonian matrix of the SIAM.
hybrid_z(z, e_bath, hopping_sqr)	Hybridization function of the impurity.