Synergistic Polaron Formation in the Hubbard-Holstein Model at Small Doping

TL;DR

This study investigates how dynamical Holstein phonons influence the Hubbard model at small doping, revealing a synergistic enhancement of spin correlations and polaron formation, but a decrease in superconducting transition temperature.

Contribution

It demonstrates the significant role of non-local antiferromagnetic correlations in amplifying electron-phonon interactions within the Hubbard-Holstein model.

Findings

Electron-phonon coupling enhances non-local spin correlations.

Polaron formation occurs at moderate coupling strengths.

Superconducting transition temperature decreases despite increased pairing interaction.

Abstract

We study the effect of dynamical Holstein phonons on the physics of the Hubbard model at small doping using the dynamical cluster approximation on a $2\times2$ cluster. Non-local antiferromagnetic correlations are found to significantly enhance the electron-phonon coupling, resulting in polaron formation for moderate coupling strengths. At finite doping, the electron-phonon coupling is found to strongly enhance the non-local spin correlations, indicating a synergistic interplay between the electron-phonon coupling and antiferromagnetic correlations. Although it enhances the pairing interaction, the electron-phonon coupling is found to decrease the superconducting transition temperature, due to the reduction in the quasiparticle fraction.