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

TL;DR

This paper investigates the Emery-Kivelson line and Wilson ratio universality in the spin anisotropic Kondo model across multiple channels, revealing conditions for universality and proposing new experimental ratios.

Contribution

It demonstrates the existence of the Emery-Kivelson line for any number of channels and clarifies the conditions under which the Wilson ratio is universal or not.

Findings

The EK line exists for all k, but maps to free fermions only for k=1,2.

Wilson ratio is universal for k=1,2 but not for k>2.

Low temperature resistivity correction is unaffected by spin anisotropy for any k.

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.