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

Abstract

We consider the two channel Kondo model in the Emery-Kivelson approach, and calculate the total susceptibility enhancement due to the impurity $χ_{imp}=χ-χ_{bulk}$. We find that $χ_{imp}$ 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 $χ_{imp} \sim \log {1 \over T}$, $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 $χ_{imp}\sim log {1 \over h}$ is also recovered.