Abstract
An exact diagonalization study of the 2D Hubbard model extended with nearest neighbor (NN) phonon mediated interaction shows an interplay between on-site Coulomb interaction and intersite electron-phonon interaction. Initially, phonon mediated interaction between electrons is suppressed by onsite Coulomb repulsion. But after certain larger strength (depending on U) of phonon mediated interaction there is an effective attraction between electrons which forms onsite bipolaron (S0) and neighboring site bipolaron (S1).
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