Friedel sum rule for an interacting multiorbital quantum dot

TL;DR

This paper derives a generalized Friedel sum rule for multiorbital quantum dots, connecting electron phase shifts to spectral density changes while accounting for many-body correlations.

Contribution

It introduces a new Friedel sum rule applicable to interacting multiorbital quantum dots, extending previous single-orbital formulations.

Findings

The sum rule accurately relates phase shifts to spectral density displacements.

It incorporates all many-body correlation effects.

Applicable to complex quantum dot systems with multiple orbitals.

Abstract

A generalized Friedel sum rule is derived for a quantum dot with internal orbital and spin degrees of freedom. The result is valid when all many-body correlations are taken into account and it links the phase shift of the scattered electron to the displacement of its SPECTRAL density into the dot.