On Emery-Kivelson line and universality of Wilson ratio of spin anisotropic Kondo model

Abstract

Yuval-Anderson's scaling analysis and Affleck-Ludwig's Conformal Field Theory approach are applied to the $k$ channel {\em spin anisotropic} Kondo model. Detailed comparisons with the available Emery-Kivelson's Abelian Bosonization approaches are made. It is shown that the EK line exists for any $k$, although it can be mapped to free fermions only when $k=1$ or $2$. The Wilson ratio is universal if $k=1$ or $2$, but {\em not} universal if $k>2$. The leading low temperature correction to the electron resistivity is {\em not} affected by the spin anisotropy for {\em any} $k$. A new universal ratio for $k>2$ is proposed to compare with experiments.