A local moment approach to the degenerate Anderson impurity model

TL;DR

This paper extends the local moment approach to the SU(2N) Anderson impurity model, accurately capturing many-body effects and scaling spectra across energy scales, with results aligning well with numerical renormalization group data.

Contribution

The paper introduces a generalized local moment approach for the SU(2N) AIM, providing analytical results for dynamics and scaling spectra in strongly correlated regimes.

Findings

Captures many-body broadening of Hubbard satellites

Recovers exponential vanishing of Kondo scale for all N

Matches NRG results for high-frequency decay of spectra

Abstract

The local moment approach is extended to the orbitally-degenerate [SU(2N)] Anderson impurity model (AIM). Single-particle dynamics are obtained over the full range of energy scales, focussing here on particle-hole symmetry in the strongly correlated regime where the onsite Coulomb interaction leads to many-body Kondo physics with entangled spin and orbital degrees of freedom. The approach captures many-body broadening of the Hubbard satellites, recovers the correct exponential vanishing of the Kondo scale for all N, and its universal scaling spectra are found to be in very good agreement with numerical renormalization group (NRG) results. In particular the high-frequency logarithmic decays of the scaling spectra, obtained here in closed form for arbitrary N, coincide essentially perfectly with available numerics from the NRG. A particular case of an anisotropic Coulomb interaction, in which the model represents a system of N `capacitively-coupled' SU(2) AIMs, is also discussed. Here the model is generally characterised by two low-energy scales, the crossover between which is seen directly in its dynamics.