Small polaron formation in many-particle states of the Hubbard-Holstein model: The one-dimensional case

TL;DR

This study explores how polarons form in a one-dimensional Hubbard-Holstein model with strong local electron repulsion, revealing different formation conditions in adiabatic and antiadiabatic regimes through numerical analysis.

Contribution

It provides a detailed numerical analysis of polaron formation conditions in the Hubbard-Holstein model, distinguishing between adiabatic and antiadiabatic regimes.

Findings

Polaron formation in the adiabatic regime requires energy gain overcoming electronic energy.

In the antiadiabatic regime, large ionic displacement drives polaron formation.

Dynamical properties vary significantly between weak and moderate coupling regimes.

Abstract

We investigate polaron formation in a many-electron system in the presence of a local repulsion sufficiently strong to prevent local-bipolaron formation. Specifically, we consider a Hubbard-Holstein model of interacting electrons coupled to dispersionless phonons of frequency $\omega_0$. Numerically solving the model in a small one-dimensional cluster, we find that in the nearly adiabatic case $\omega_0 < t$, the necessary and sufficient condition for the polaronic regime to occur is that the energy gain in the atomic (i.e., extremely localized) regime ${\cal E}_{pol}$ overcomes the energy of the purely electronic system $ {\cal E}_{el}$. In the antiadiabatic case, $\omega_0 > t$, polaron formation is instead driven by the condition of a large ionic displacement $g/\omega_0 >1$ ($g$ being the electron-phonon coupling). Dynamical properties of the model in the weak and moderately strong coupling regimes are also analyzed.