The zero-temperature transconductance of the N-channel SO(M) topological Kondo model is expressed through the modular S-matrix of SO(M) at level 2N, and the finite-temperature correction exponent changes between N=1 and N at least 2.
On the Emery-Kivelson Solution of the two channel Kondo problem
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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.
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Multichannel topological Kondo models and their low-temperature conductances
The zero-temperature transconductance of the N-channel SO(M) topological Kondo model is expressed through the modular S-matrix of SO(M) at level 2N, and the finite-temperature correction exponent changes between N=1 and N at least 2.