Impurity Diagonalization

The ed_diag provides a single interface to all the different diagonalization procedures available in the code. This is used in the ed_main Fortran API.

• Impurity diagonalization interface

Normal mode

This set of modules implements the exact diagonalization of the single impurity problems 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.

• Exact Diagonalization

Superconductive mode

This set of modules implements the exact diagonalization of the single impurity problems assuming \(\vec{Q}\equiv S_z=N_\uparrow-N_\downarrow\).

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

• Exact Diagonalization

Non-SU(2) mode

This set of modules implements the exact diagonalization of the single impurity problems 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.

• Exact Diagonalization