Charge instabilities and electron-phonon interaction in the Hubbard-Holstein model

TL;DR

This paper studies how electron-electron interactions in the Hubbard-Holstein model influence electron-phonon coupling, revealing that correlations screen the coupling and alter the instability from charge-density waves to phase separation.

Contribution

It provides a detailed analysis of the screening effect of electron-electron interactions on electron-phonon coupling within the Hubbard-Holstein model using the Gutzwiller approximation.

Findings

Electron-electron correlations screen electron-phonon coupling.

Charge-density wave instability is replaced by phase separation.

Screening is more effective at large momenta.

Abstract

We consider the Hubbard-Holstein model in the adiabatic limit to investigate the effects of electron-electron interactions on the electron-phonon coupling. To this aim we compute at any momentum and filling the static charge susceptibility of the Hubbard model within the Gutzwiller approximation and we find that electron-electron correlations effectively screen the electron coupling to the lattice. This screening is more effective at large momenta and, as a consequence, the charge-density wave phase due to the usual Peierls instability of the Fermi surface momenta is replaced by a phase-separation instability when the correlations are sizable.