Impurity Reduced Density Matrix

The ed_rdm provides a single interface to the evaluation of the Reduced Density Matrix (RDM) \(\rho_{imp}={\rm Tr}_{bath}\rho\) for any value of ed_mode. This is used in the ed_main Fortran API.

• Impurity RDM

Normal mode

This module implements the evaluation of impurity RDM assuming the conserved quantum numbers are \(\vec{Q}=\left[\vec{N}_\uparrow,\vec{N}_\downarrow \right]\). 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.

• Reduced Density Matrix

Superconductive mode

This module implements the evaluation of impurity RDM assuming \(\vec{Q}\equiv S_z=N_\uparrow-N_\downarrow\).

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

• Reduced Density Matrix

Non-SU(2) mode

This module implements the evaluation of impurity RDM 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.

• Reduced Density Matrix