Validity of the local self-energy approximation: Application to coupled quantum impurities

TL;DR

This paper evaluates the effectiveness of the local self-energy approximation, similar to DMFT, in modeling coupled quantum impurities, identifying its successes in certain regimes and failures in others.

Contribution

It systematically compares impurity-DMFT results with exact methods to delineate its applicability to inhomogeneous quantum impurity systems.

Findings

Impurity-DMFT captures dilute impurity limits.

Fails to describe RKKY-dominated singlet formation.

Succeeds in modeling underscreened Kondo physics.

Abstract

We examine the quality of the local self-energy approximation, applied here to models of multiple quantum impurities coupled to an electronic bath. The local self-energy is obtained by solving a single-impurity Anderson model in an effective medium that is determined self-consistently, similar to the dynamical mean-field theory (DMFT) for correlated lattice systems. By comparing to exact results obtained using the numerical renormalization group, we determine situations where "impurity-DMFT" is able to capture the physics of highly inhomogeneous systems, and those cases where it fails. For two magnetic impurities separated in real-space, the onset of the dilute limit is captured, but RKKY-dominated inter-impurity singlet formation cannot be described. For parallel quantum dot devices, impurity-DMFT succeeds in capturing underscreened Kondo physics by self-consistent generation of a critical pseudogapped effective medium. However, the quantum phase transition between high- and low-spin states on tuning interdot coupling cannot be described.