The beta function of the multichannel Kondo model

TL;DR

This paper calculates the exact beta function of the multichannel Kondo model in the large N limit, revealing non-Fermi liquid behavior and enabling analysis of low-temperature thermodynamics.

Contribution

It provides an exact calculation of the beta function for the multichannel Kondo model at large N, showing a zero at finite coupling and connecting to thermodynamic properties.

Findings

Identifies a zero in the beta function indicating non-Fermi liquid behavior.

Enables analysis of low-temperature thermodynamics via a variational principle.

Provides insights into the non-crossing approximation's thermodynamics.

Abstract

The beta function of the multichannel Kondo model is calculated exactly in the limit of large spin N and channel number M=gamma*N, with constant gamma. There are no corrections in any finite order of 1/N. One zero is found at a finite coupling strength, showing directly the Non--Fermi liquid behavior of the model. This renormalization group flow allows to introduce a variational principle for the entropy, to obtain the low temperature thermodynamics. Such in particular the low temperature thermodynamics of the non--crossing approximation to the Kondo model becomes accessible.