Absence of two energy scales in the two-impurity Kondo model

TL;DR

This paper challenges the common belief that two distinct energy scales exist in the two-impurity Kondo model, demonstrating that a fundamental scaling law contradicts the presence of a second energy scale.

Contribution

It shows that the expected second energy scale does not exist in the two-impurity Kondo model, based on an exact scaling law in the magnetic limit.

Findings

Contradicts the assumption of two energy scales in the model.

Demonstrates the exactness of the scaling law for large bandwidth.

Questions the traditional understanding of impurity interactions.

Abstract

It is believed that the successive antiferromagnetic scattering of the conduction electrons on two magnetic impurities in a metal, induces a magnetic interaction between the impurities which sets an energy scale for the system, in addition to the Kondo temperature. However, it is shown here that this contradicts a scaling law for the two-impurity Anderson model in the magnetic limit which becomes exact for a large bandwidth.