Exact scaling functions of the multichannel Kondo model

TL;DR

This paper derives explicit analytical scaling functions for the multichannel Kondo model at zero temperature, simplifying complex integral equations to differential equations, and extends the approach to finite temperatures and related models.

Contribution

It provides a novel, exact analytical solution for the universal scaling functions of the multichannel Kondo model, including finite temperature effects.

Findings

Explicit zero-temperature scaling functions derived

Simplification of integral equations to differential equations

Extension to finite temperature and related models

Abstract

We reinvestigate the large degeneracy solution of the multichannel Kondo problem, and show how in the universal regime the complicated integral equations simplifying the problem can be mapped onto a first order differential equation. This leads to an explicit expression for the full zero-temperature scaling functions at - and away from - the intermediate non Fermi Liquid fixed point, providing complete analytic information on the universal low - and intermediate - energy properties of the model. These results also apply to the widely-used Non Crossing Approximation of the Anderson model, taken in the Kondo regime. An extension of this formalism for studying finite temperature effects is also proposed and offers a simple approach to solve models of strongly correlated electrons with relevance to the physics of heavy fermion compounds.