Exact perturbative solution of the Kondo problem

TL;DR

This paper provides an exact perturbative solution to the anisotropic Kondo problem by connecting it to the boundary sine-Gordon model and utilizing Jack polynomials, offering a precise analytical approach.

Contribution

It introduces a novel method linking the anisotropic Kondo problem to the boundary sine-Gordon model for arbitrary spin, enabling exact solutions.

Findings

Explicit evaluation of integrals in the Coulomb gas representation

Development of a general approach relating Kondo problem to sine-Gordon model

Exact perturbative solution using Jack polynomials

Abstract

We explicitly evaluate the infinite series of integrals that appears in the "Anderson-Yuval" reformulation of the anisotropic Kondo problem in terms of a one-dimensional Coulomb gas. We do this by developing a general approach relating the anisotropic Kondo problem of arbitrary spin with the boundary sine-Gordon model, which describes impurity tunneling in a Luttinger liquid and in the fractional quantum Hall effect. The Kondo solution then follows from the exact perturbative solution of the latter model in terms of Jack polynomials.