Critical theory of overscreened Kondo fixed points

Abstract

The low-temperature fixed point of the Kondo model, for k bands and a spin- s impurity, is well understood by Nozières' Fermi liquid theory for k ⩽ 2 s. However when k > 2 s, a new type of non-trivial fixed point is known to occur. We study this fixed point using higher-level Kac-Moody conformal field theory and Cardy's approach to boundary critical phenomena. The specific heat and magnetization are shown to be determined by the leading irrelevant operator and the corresponding critical exponents are obtained exactly. The Wilson ratio is argued to be universal and its exact value is also calculated. The asymptotic finite-size spectrum is determined. Thermodynamic exponents agree precisely with the Bethe ansatz; for k = 2, s = 1 2 , the Wilson ratio also agrees well with the approximate value obtained from the Bethe ansatz; the slope of the β-function agrees with the perturbative result in the large- k limit and the finite-size spectrum agrees excellently with approximate results obtained previously by Wilson's numerical renormalization group method in the case k = 2, s = 1 2 .