Overscreened multi-channel SU(N) Kondo model : large-N solution and Conformal Field Theory

TL;DR

This paper analyzes the overscreened multichannel SU(N) Kondo model using conformal field theory and large-N techniques, revealing universal non-Fermi liquid behavior and scaling properties at low temperatures.

Contribution

It provides a large-N solution and conformal field theory analysis of the overscreened SU(N) Kondo model, deriving universal low-temperature properties and scaling functions.

Findings

Universal low-temperature thermodynamics and transport properties derived.

Spectral densities exhibit universal scaling in ω/T.

Residual entropy and resistivity computed in the large-N limit.

Abstract

The multichannel Kondo model with SU(N) spin symmetry and SU(K) channel symmetry is considered. The impurity spin is chosen to transform as an antisymmetric representation of SU(N), corresponding to a fixed number of Abrikosov fermions $\sum_{\alpha}f_{\alpha}^{\dagger}f_{\alpha}=Q$. For more than one channel (K>1), and all values of N and Q, the model displays non-Fermi behaviour associated with the overscreening of the impurity spin. Universal low-temperature thermodynamic and transport properties of this non-Fermi liquid state are computed using conformal field theory methods. A large-N limit of the model is then considered, in which K/N and Q/N are held fixed. Spectral densities satisfy coupled integral equations in this limit, corresponding to a (time-dependent) saddle-point. A low frequency, low-temperature analysis of these equations reveals universal scaling properties in the variable $\omega/T$, also predicted from conformal invariance. The universal scaling form is obtained analytically and used to compute the low-temperature universal properties of the model in the large-N limit, such as the T=0 residual entropy and residual resistivity, and the critical exponents associated with the specific heat and susceptibility. The connections with the ``non-crossing approximation'' and the previous work of Cox and Ruckenstein are discussed.