On the applicability of bosonization and the Anderson-Yuval methods at the strong-coupling limit of quantum impurity problems

TL;DR

This paper evaluates the effectiveness of bosonization and the Anderson-Yuval methods at strong coupling in quantum impurity models, highlighting the importance of conduction-electron density of states renormalization based on fixed point stability.

Contribution

It establishes a criterion for when DoS renormalization is necessary in these methods, improving their accuracy at strong coupling.

Findings

DoS renormalization is crucial for unstable fixed points.

Bosonization can be redundant when a local decoupled entity forms.

The criterion enhances method applicability at strong coupling.

Abstract

The applicability of bosonization and the Anderson-Yuval (AY) approach at strong coupling is investigated by considering two generic impurity models: the multichannel interacting resonant-level and the anisotropic Kondo models. The two methods differ in the renormalization of the conduction-electron density of states (DoS) near the impurity site. Reduction of the DoS, absent in bosonization but accounted for in the AY approach, is shown to be vital in some models yet redundant in others. The criterion being the stability of the strong-coupling fixed point. Renormalization of the DoS is essential for an unstable fixed point, but redundant when a decoupled entity with local dynamics is formed. This rule can be used to boost the accuracy of both methods at strong coupling.