Kondo effect in the hierarchical s-d model

TL;DR

This paper investigates a hierarchical s-d model to analyze the Kondo effect, extending previous work on hierarchical models and providing insights into magnetic impurity interactions at very low temperatures.

Contribution

It introduces a hierarchical version of the s-d model and extends the analysis of the Kondo effect within this framework, simplifying previous hierarchical models.

Findings

Hierarchical s-d model exhibits similar behavior to hierarchical Andrei model.

Analysis confirms the finite magnetic susceptibility at zero temperature.

Model provides a simpler approach to studying Kondo physics hierarchically.

Abstract

The s-d model describes a chain of spin-1/2 electrons interacting magnetically with a two-level impurity. It was introduced to study the Kondo effect, in which the magnetic susceptibility of the impurity remains finite in the 0-temperature limit as long as the interaction of the impurity with the electrons is anti-ferromagnetic. A variant of this model was introduced by Andrei, which he proved was exactly solvable via Bethe Ansatz. A hierarchical version of Andrei's model was studied by Benfatto and the authors. In the present letter, that discussion is extended to a hierarchical version of the s-d model. The resulting analysis is very similar to the hierarchical Andrei model, though the result is slightly simpler.