Phonon-Mediated Electron-Phonon Interaction in Hubbard-Holstein Model

We explore the influence of inter-site electron-phonon (EP) interaction lambda on some ground state and finite temperature properties of Hubbard-Holstein model using exact diagonalization technique. Both the adiabatic and non-adiabatic limits have been considered. Results show that the EP correlation function chi increases gradually for the adiabatic case with lambda while a sharp transition is observed at lambda = lambda(c)(U/t) for the non-adiabatic case. On-site (S0) and inter-site (S1) bipolarons are formed which tend to bind at lambda >= lambda c(U/t). Schematic phase diagram has been shown. Entropy calculations show that the system goes to a more ordered state when lambda >= lambda(c)(U/t) due to the formation of EP pairs. Broad peaks are observed in the specific heat curves which move to higher temperature region with lambda suggesting an effective increase in exchange energy.