Slave-boson approach to the infinite-U Anderson-Holstein impurity model

TL;DR

This paper investigates the infinite-U Anderson-Holstein impurity model using a slave boson approach combined with large degeneracy expansion, revealing how electron-phonon interactions influence charge susceptibility and Kondo temperature.

Contribution

It introduces a combined slave boson and 1/N expansion method to analyze the impurity model, highlighting the role of Gaussian fluctuations in phonon dynamics.

Findings

Spin susceptibility remains unaffected by electron-phonon interaction.

Charge susceptibility is renormalized, leading to an increased Kondo temperature.

Gaussian fluctuations are crucial for accurate phonon propagator analysis.

Abstract

The infinite-$U$ Anderson-Holstein impurity model is studied with a focus on the interplay between the strong electron correlation and the weak electron-phonon interaction. The slave boson method has been employed in combination with the large degeneracy expansion (1/N) technique. The charge and spin susceptibilities and the phonon propagator are obtained in the approximation scheme where the saddle point configuration and the Gaussian 1/N fluctuations are taken into account. The spin susceptibility is found not to be renormalized by electron-phonon interaction, while the charge susceptibility is renormalized. From the renormalized charge susceptibility the Kondo temperature is found to increase by the electron-phonon interaction. It turns out that the bosonic 1/N Gaussian fluctuations play a very crucial role, in particular, for the phonon propagator.