Electron-phonon interaction in Strongly Correlated Systems

TL;DR

This paper reviews how strong electron correlations influence electron-phonon interactions in the Hubbard-Holstein model, highlighting their significance in high-temperature superconductors and related phenomena.

Contribution

It provides a comprehensive analysis of the effects of strong correlations on electron-phonon interactions, emphasizing non-conventional signatures and the role of magnetic correlations.

Findings

Electron-phonon interactions remain significant despite strong correlations.

Phonons influence high-energy properties and can induce phase separation.

Antiferromagnetic correlations enhance electron-phonon effects by reducing screening.

Abstract

The Hubbard-Holstein model is a simple model including both electron-phonon interaction and electron-electron correlations. We review a body of theoretical work investigating the effects of strong correlations on the electron-phonon interaction. We focus on the regime, relevant to high-T_c superconductors, in which the electron correlations are dominant. We find that the electron-phonon interaction can still have important signatures, even if many anomalies appear, and the overall effect is far from conventional. In particular in the paramagnetic phase the effects of phonons are much reduced in the low-energy properties, while the high-energy physics can be strongly affected by phonons. Moreover, the electron-phonon interaction can still give rise to important effects, like phase separation and charge-ordering, and it assumes a predominance of forward scattering even if the bare interaction is assumed to be local (momentum independent). Antiferromagnetic correlations reduce the screening effects due to electron-electron interactions and revive the electron-phonon effects.