Admittance of the SU(2) and SU(4) Anderson quantum RC circuits

TL;DR

This paper investigates the charge relaxation resistance in SU(2) and SU(4) Anderson quantum RC circuits using Bethe ansatz and perturbation theory, revealing peaks in resistance related to Kondo and valence-fluctuation regimes.

Contribution

It provides a detailed analysis of charge relaxation resistance in SU(2) and SU(4) Anderson models, including analytical and numerical results, extending understanding of quantum RC circuits.

Findings

Peak in Rq in Kondo regime matches NRG results

Persistent peak in Rq in valence-fluctuation region with max h/2e^2

Giant peak in Rq found in SU(4) model

Abstract

We study the Anderson model as a description of the quantum RC circuit for spin-1/2 electrons and a single level connected to a single lead. Our analysis relies on the Fermi liquid nature of the ground state which fixes the form of the low energy effective model. The constants of this effective model are extracted from a numerical solution of the Bethe ansatz equations for the Anderson model. They allow us to compute the charge relaxation resistance Rq in different parameter regimes. In the Kondo region, the peak in Rq as a function of the magnetic field is recovered and proven to be in quantitative agreement with previous numerical renormalization group results. In the valence-fluctuation region, the peak in Rq is shown to persist, with a maximum value of h/2e^2, and an analytical expression is obtained using perturbation theory. We extend our analysis to the SU(4) Anderson model where we also derive the existence of a giant peak in the charge relaxation resistance.