Electron Phonon Interaction In Hubbard Model

Hubbard model having on-site electron-phonon interaction and inter-site phonon mediated interaction has been studied by exact diagonalization method. Results show 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 a certain larger strength, both on-site and neighboring site electron-phonon coupling occurs.