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

We investigate polaron formation in a many-electron system in the presence of a local repulsion sufficiently strong to prevent local-bipolaron formati on. Specifically, we consider a Hubbard-Holstein model of interacting elect rons coupled to dispersionless phonons of frequency omega(0). Numerically s olving the model in a small one-dimensional cluster, we find that in the ne arly adiabatic case omega(0) < t, the necessary and sufficient condition fo r the polaronic regime to occur is that the energy gain in the atomic (i.e. , extremely localized) regime E-pol overcomes the energy of the purely elec tronic system E-el. In the antiadiabatic case, omega(0) > t, polaron format ion is instead driven by the condition of a large ionic displacement g/omeg a(0) > 1 (g being the electron-phonon coupling). Dynamical properties of th e model in the weak and moderately strong coupling regimes are also analyze d.