Electron-phonon vertex in the two-dimensional one-band Hubbard model

TL;DR

This study uses quantum Monte Carlo methods to investigate how electronic correlations in a two-dimensional Hubbard model influence the effective electron-phonon coupling, revealing suppression at low U and enhancement in forward scattering at high U.

Contribution

It provides a detailed analysis of the evolution of electron-phonon interactions across different correlation regimes, highlighting the role of vertex corrections in strongly correlated systems.

Findings

Electron-phonon coupling is suppressed at low U due to screening.

At high U, forward scattering coupling increases significantly.

Vertex corrections become dominant in the strong-correlation regime.

Abstract

Using quantum Monte Carlo techniques, we study the effects of electronic correlations on the effective electron-phonon (el-ph) coupling in a two-dimensional one-band Hubbard model. We consider a momentum-independent bare ionic el-ph coupling. In the weak- and intermediate-correlation regimes, we find that the on-site Coulomb interaction $U$ acts to effectively suppress the ionic el-ph coupling at all electron- and phonon- momenta. In this regime, our numerical simulations are in good agreement with the results of perturbation theory to order $U^2$. However, entering the strong-correlation regime, we find that the forward scattering process stops decreasing and begins to substantially increase as a function of $U$, leading to an effective el-ph coupling which is peaked in the forward direction. Whereas at weak and intermediate Coulomb interactions, screening is the dominant correlation effect suppressing the el-ph coupling, at larger $U$ values irreducible vertex corrections become more important and give rise to this increase. These vertex corrections depend crucially on the renormalized electronic structure of the strongly correlated system.