Interplay Between Electron-Phonon Interaction and Hubbard Repulsion: an Exact Approach

An exact diagonalization study of the Hubbard model having both on-site and inter-site electron-phonon interactions in the weak-coupling limit shows that on-site electron-phonon interaction generates an effective attraction between electrons which forms an on-site bipolaron (S0). On the other hand, electron-phonon interaction between nearest neighbor sites forms both on-site and inter-site bipolaron (S1). However, the formation of both S0 and S1 bipolarons is suppressed by on-site Coulomb repulsion. Suppression is more in the adiabatic regime of phonon energy. Effective bipolaronic hopping amplitude depends on the Coulomb repulsion.