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

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 ${\mathcal{E}}_{pol}$ overcomes the energy of the purely electronic system ${\mathcal{E}}_{el}$. 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.

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