Charge fluctuations and electron-phonon interaction in the finite-$U$ Hubbard model

TL;DR

This study uses a gaussian expansion within the finite-U slave-bosons formalism to analyze how electron correlations affect the momentum structure of the electron-phonon vertex in the Hubbard model, revealing key features like suppression of large momentum scattering.

Contribution

It introduces a novel application of gaussian expansion in the slave-bosons formalism to explore electron-phonon interactions across different U and n values in the Hubbard model.

Findings

Large momentum scattering is suppressed by electronic correlations.

A small-q peak structure emerges, characterized by a cutoff q_c.

The phase diagram of Z_MF and q_c aligns with numerical analyses.

Abstract

In this paper we employ a gaussian expansion within the finite-$U$ slave-bosons formalism to investigate the momentum structure of the electron-phonon vertex function in the Hubbard model as function of $U$ and $n$. The suppression of large momentum scattering and the onset a small-${\bf q}$ peak structure, parametrized by a cut-off $q_c$, are shown to be essentially ruled by the band narrowing factor $Z_{\rm MF}$ due to the electronic correlation. A phase diagram of $Z_{\rm MF}$ and $q_c$ in the whole $U$-$n$ space is presented. Our results are in more than qualitative agreement with a recent numerical analysis and permit to understand some anomalous features of the Quantum Monte Carlo data.