Polarons and bipolarons in a four-site periodic chain of spinless fermions

The nature of polarons is studied in a four-site model containing one and two spinless fermions in the presence of fermion-phonon (f-ph) interactions and intersite hopping. In the four-site one-fermion model a small-to-large polaron transition associated with a sudden increase in polaronic hopping and a decrease in the polaronic binding energy is observed as the f-ph strength decreases below a particular value. The role of the modified Lang-Firsov transformation and two-phonon coherent states In lowering the energy of the system is discussed. For the four-site two-fermion system the nature and stability of bipolaronic states with the variation of f-ph coupling strength are studied. It is observed that bipolaronic states are stable only in the presence of intersite f-ph interactions.