The Kondo impurity in the large spin limit

TL;DR

This paper introduces an analytic approach combining 1/s expansion with renormalization group techniques to study the large spin limit of the Kondo impurity problem, providing insights into thermodynamics and spectral properties.

Contribution

It presents a novel analytic method for the Kondo problem at large spin, enabling the study of intermediate scales and properties not easily accessible by previous methods.

Findings

Analytic expressions for impurity entropy and susceptibility agree with Bethe ansatz.

Computed impurity spectral function, resistivity, and screening cloud profile.

Accessed non-Fermi-liquid overscreened fixed point for K > 2s.

Abstract

The Kondo problem, which describes the interaction of a spin $s$ magnetic impurity with a free Fermi gas, is a classic example of strongly coupled physics. Historically, the problem has been solved by Wilson's numerical renormalization group and later by Bethe ansatz. In this paper, we present an alternate analytic solution of the Kondo problem that combines an expansion in $1/s$ with the renormalization group. We study both the case of an impurity interacting with a single channel $K=1$ of fermions in the $s \rightarrow \infty$ limit and the case with $K$ channels in the double-scaling limit $K \rightarrow \infty$, $s \to \infty$, $K/s$ fixed. Our approach allows us to describe analytically intermediate scales of the Kondo problem at large $s$ and compute thermodynamic observables such as the impurity entropy and susceptibility. We find these observables to agree with the Bethe ansatz results. We also compute the impurity spectral function, finite temperature resistivity and the Kondo screening cloud profile, properties that are not easily accessible from Bethe ansatz. Notably, in the regime $K > 2s$ we access the "non-Fermi-liquid" overscreened fixed point of the multichannel Kondo problem.