Impurity Green’s functions

The ed_greens_functions and ed_chi_functions (only for ed_mode = normal) provide two simple interfaces to all the different dynamical response functions calculation procedures available in the code. This is used in the ed_main Fortran API.

• Impurity response functions interface

Normal mode

This set of modules implements the calculations of impurity dynamical response functions, e.g. the Green’s functions and different susceptibilities, assuming \(\vec{Q}=\left[\vec{N}_\uparrow,\vec{N}_\downarrow \right]\). Where \(\vec{N}_\sigma=N_\sigma\) if the total number of electrons with spin \(\sigma\) is conserved (ed_total_ud = T ) or \(\vec{N}_\sigma=[ N_{1\sigma},\dots,N_{N_{orb}\sigma} ]\) if the number of electrons in the orbital \(\alpha=1,\dots,N_{orb}\) and spin \(\sigma\) is conserved (ed_total_ud = F).

This case corresponds to the normal phase in presence of spin conservation, possibly reduced to \(U(1)\) in presence of long range magnetic order along \(z\) quantization axis of the spin operator.

• Green’s Function calculation
• Spin Susceptibility
• Density Susceptibility
• Pair Susceptibility
• Exciton Susceptibility

Superconductive mode

This set of modules implements the calculations of impurity dynamical response functions, e.g. the Green’s functions, assuming \(\vec{Q}\equiv S_z=N_\uparrow-N_\downarrow\).

This case corresponds to the superconductive phase with \(s-\) wave pairing.

• Green’s Function calculation

Non-SU(2) mode

This set of modules implements the calculations of impurity dynamical response functions, e.g. the Green’s functions, assuming \(\vec{Q}\equiv N_{tot}=N_\uparrow+N_\downarrow\).

This case corresponds to the normal phase in the absence of spin conservation, as for instance in presence of Spin-Orbit coupling.

• Green’s Function calculation