On-site and inter-site electron–phonon interaction in 2D Hubbard model

An exact diagonalization study of Hubbard model having on-site electron–phonon interaction and inter-site phonon mediated interaction shows that on-site electron–phonon interaction generates an effective attraction between electrons which eventually forms on-site bipolaron. On the other hand, phonon mediated interaction between electrons at nearest-neighbor sites is suppressed by on-site Coulomb repulsion initially, but at certain larger strength this interaction strengthen the on-site electron–phonon interaction. There is also formation of neighboring-site bipolaron. Results show that interplay between electron–electron interaction and electron–phonon interaction is very much relevant.