The strong-coupling limit of a Kondo spin coupled to a mesoscopic quantum dot: effective Hamiltonian in the presence of exchange correlations

TL;DR

This paper derives an effective Hamiltonian for a Kondo spin coupled to a chaotic quantum dot with exchange interactions, revealing renormalized couplings and new terms, validated by numerical results.

Contribution

It introduces a novel effective Hamiltonian in the strong-coupling limit accounting for exchange correlations in the quantum dot.

Findings

Effective Hamiltonian includes renormalized exchange coupling.

New interaction terms appear beyond conventional models.

Eigenenergies match numerical results in strong-coupling regime.

Abstract

We consider a Kondo spin that is coupled antiferromagnetically to a large chaotic quantum dot. Such a dot is described by the so-called universal Hamiltonian and its electrons are interacting via a ferromagnetic exchange interaction. We derive an effective Hamiltonian in the limit of strong Kondo coupling, where the screened Kondo spin effectively removes one electron from the dot. We find that the exchange coupling constant in this reduced dot (with one less electron) is renormalized and that new interaction terms appear beyond the conventional terms of the strong-coupling limit. The eigenenergies of this effective Hamiltonian are found to be in excellent agreement with exact numerical results of the original model in the limit of strong Kondo coupling.