Kondo effect in a fermionic hierarchical model

TL;DR

This paper introduces an exactly solvable fermionic hierarchical model inspired by the Kondo effect, demonstrating how antiferromagnetic interactions lead to finite magnetic susceptibility at zero temperature, unlike ferromagnetic interactions.

Contribution

The paper presents a new exactly solvable hierarchical fermionic model that captures the Kondo effect, highlighting its non-perturbative nature and solvability due to its hierarchical structure.

Findings

Antiferromagnetic interaction results in finite susceptibility at zero temperature.

Ferromagnetic interaction causes divergence in susceptibility.

Model is exactly solvable due to its fermionic and hierarchical properties.

Abstract

In this paper, a fermionic hierarchical model is defined, inspired by the Kondo model, which describes a 1-dimensional lattice gas of spin-1/2 electrons interacting with a spin-1/2 impurity. This model is proved to be exactly solvable, and is shown to exhibit a Kondo effect, i.e. that, if the interaction between the impurity and the electrons is antiferromagnetic, then the magnetic susceptibility of the impurity is finite in the 0-temperature limit, whereas it diverges if the interaction is ferromagnetic. Such an effect is therefore inherently non-perturbative. This difficulty is overcome by using the exact solvability of the model, which follows both from its fermionic and hierarchical nature.