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 ω ₀. Numerically solving the model in a small one-dimensional cluster, we find that in the nearly adiabatic case ω 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 ε _pol overcomes the energy of the purely electronic system ε _el. In the antiadiabatic case, ω ₀ > t, polaron formation is instead driven by the condition of a large ionic displacement g/ω ₀ < 1 (g being the electron-phonon coupling). Dynamical properties of the model in the weak and moderately strong coupling regimes are also analyzed.