Generalized Schrieffer-Wolff Transformation of 2 Kondo Impurity Problem

TL;DR

This paper extends the Schrieffer-Wolff transformation to a two-impurity Anderson model, revealing complex low-energy interactions including RKKY, superexchange, and correlated Kondo couplings.

Contribution

It introduces a generalized transformation method that captures higher-order interactions in the two-impurity Kondo problem, including novel coupling terms.

Findings

Standard Kondo Hamiltonian with scattering terms

RKKY interaction at fourth order

Discovery of superexchange and correlated Kondo couplings

Abstract

We have carried out a generalized Schrieffer-Wolff transformation of an Anderson two-impurity Hamiltonian to study the low-energy spin interactions of the system. The second-order expansion yields the standard Kondo Hamiltonian for two impurities with additional scattering terms. At fouth-order, we get the well-known RKKY interaction. In addition, we also find an antiferromagnetic superexchange coupling and a correlated Kondo coupling between the two impurities.