Interpolative approach for electron-electron and electron-phonon interactions: from the Kondo to the polaronic regime

TL;DR

This paper introduces a theoretical interpolative method to accurately analyze electronic properties of nanoscale systems with strong electron-electron and electron-phonon interactions, bridging the Kondo and polaronic regimes.

Contribution

The paper develops a generalized interpolative ansatz for the electronic self-energy applicable to systems with combined electron-electron and electron-phonon interactions, validated against established numerical methods.

Findings

The method accurately reproduces known results in weak and strong coupling limits.

It effectively captures the transition from Kondo to polaronic regimes.

Results agree with Numerical Renormalization Group data.

Abstract

We present a theoretical approach to determine the electronic properties of nanoscale systems exhibiting strong electron-electron and electron-phonon interactions and coupled to metallic electrodes. This approach is based on an interpolative ansatz for the electronic self-energy which becomes exact both in the limit of weak and strong coupling to the electrodes. The method provides a generalization of previous interpolative schemes which have been applied to the purely electronic case extensively. As a test case we consider the single level Anderson-Holstein model. The results obtained with the interpolative ansatz are in good agreement with existing data from Numerical Renormalization Group calculations. We also check our results by considering the case of the electrodes represented by a few discrete levels which can be diagonalized exactly. The approximation describes properly the transition from the Kondo regime where electron-electron interactions dominate to the polaronic case characterized by a strong electron-phonon interaction.