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

Abstract

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 $$\lambda = \lambda _{\mathrm{c}}(U/t)$$ for the non-adiabatic case. On-site (S0) and inter-site (S1) bipolarons are formed which tend to bind at $$\lambda \ge \lambda _\mathrm{c}(U/t)$$ . Schematic phase diagram has been shown. Entropy calculations show that the system goes to a more ordered state when $$\lambda \ge \lambda _\mathrm{c}(U/t)$$ 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.