A path integral approach to Anderson-Holstein model

TL;DR

This paper applies a path integral approach within a semiclassical framework to analyze the Anderson-Holstein model, deriving analytic expressions for key physical quantities and discussing isotope effects in strongly correlated systems.

Contribution

It introduces a novel path integral method to study the Anderson-Holstein model, providing analytic results and insights into isotope effects and electron-phonon interactions.

Findings

Analytic expressions for Kondo temperature renormalization

Derived phonon Green function results

Consistent comparison with numerical renormalization group

Abstract

The Anderson-Holstein model is studied in the framework of the semiclassical approximation. Analytic results for Kondo temperature renormalized by weak electron-phonon interaction and for phonon Green function are obtained, and they are interpreted from the viewpoint of dynamical mean field theory. Especially the isotope effect of the effective electron mass is discussed in the presence of strong electron correlation. The results are also compared with those by numerical renormalization group and other related works, and they are consistent with each other in their common domain of validity.