On the Emery-Kivelson Solution of the two channel Kondo problem

TL;DR

This paper analyzes the Emery-Kivelson solution of the two-channel Kondo model, revealing the behavior of impurity susceptibility and specific heat near the solvable point, and identifying the Kondo temperature's dependence on perturbations.

Contribution

It provides an exact calculation of impurity susceptibility and specific heat behavior around the Emery-Kivelson solvable point, clarifying the universal properties of the two-channel Kondo model.

Findings

Impurity susceptibility vanishes at the solvable point.

Perturbative analysis yields log(1/T) behavior for susceptibility.

Kondo temperature scales as the inverse square of the perturbation parameter.

Abstract

We consider the two channel Kondo model in the Emery-Kivelson approach, and calculate the total susceptibility enhancement due to the impurity $\chi_{imp}=\chi-\chi_{bulk}$. We find that $\chi_{imp}$ exactly vanishes at the solvable point, in a completely analogous way to the singular part of the specific heat $C_{imp}$. A perturbative calculation around the solvable point yields the generic behaviour $\chi_{imp} \sim \log {1 \over T}$, $C_{imp} \sim T\log T $ and the known universal value of the Wilson ratio $R_W={8 \over 3}$. From this calculation, the Kondo temperature can be identified and is found to behave as the inverse-square of the perturbation parameter. The small field, zero-temperature behaviour $\chi_{imp}\sim log {1 \over h}$ is also recovered.