Poor man's scaling: anisotropic Kondo and Coqblin--Schrieffer models

TL;DR

This paper derives and analyzes scaling equations for anisotropic Kondo and Coqblin--Schrieffer models with power-law density of states, providing insights into their behavior with degenerate impurity levels.

Contribution

It introduces a general scaling framework for anisotropic impurity models and applies it to derive analytical solutions for specific cases with power-law DOS.

Findings

Derived second-order scaling equations for general impurity models.

Showed how to obtain scaling equations for anisotropic Kondo models with power-law DOS.

Provided analytical solutions for the anisotropic Coqblin--Schrieffer model.

Abstract

We discuss Kondo effect for a general model, describing a quantum impurity with degenerate energy levels, interacting with a gas of itinerant electrons, and derive scaling equation to the second order for such a model. We show how the scaling equation for the spin-anisotropic Kondo model with the power law density of states (DOS) for itinerant electrons follows from the general scaling equation. We introduce the anisotropic Coqblin--Schrieffer model, apply the general method to derive scaling equation for that model for the power law DOS, and integrate the derived equation analytically.