Renormalization of the electron-phonon coupling in the one-band Hubbard model

TL;DR

This study examines how electronic correlations in the one-band Hubbard model influence electron-phonon interactions, revealing suppression at low temperatures and a reentrant increase at higher temperatures due to phase behavior.

Contribution

It provides a detailed analysis of the temperature-dependent renormalization of electron-phonon coupling in the Hubbard model using slave-boson methods, highlighting novel reentrant behavior.

Findings

U suppresses electron-phonon coupling at low T

Coupling increases with U at higher T

Reentrant phase transition influences coupling behavior

Abstract

We investigate the effect of electronic correlations on the coupling of electrons to Holstein phonons in the one-band Hubbard model. We calculate the static electron-phonon vertex within linear response of Kotliar-Ruckenstein slave-bosons in the paramagnetic saddle-point approximation. Within this approach the on-site Coulomb interaction U strongly suppresses the coupling to Holstein phonons at low temperatures. Moreover the vertex function does not show particularly strong forward scattering. Going to larger temperatures kT\sim t we find that after an initial decrease with U, the electron-phonon coupling starts to increase with U, confirming a recent result of Cerruti, Cappelluti, and Pietronero. We show that this behavior is related to an unusual reentrant behavior from a phase separated to a paramagnetic state upon decreasing the temperature.