Perfect coherent shift of bound pairs in strongly correlated systems

In the present work we extend the concept of coherent shift for the extended Bose-Hubbard model and Fermi-Hubbard model. We present two types of local bound pair (BP) for Bose system and one type for Fermi system. It is shown exactly that the perfect coherent shift can be achieved in such models. We find that for a Bose on-site BP, the perfect coherent shift condition depends on the nearest-neighbor interaction strength and the momentum of the incident single particle wavepacket, while for the other two types of BPs, it is independent of the initial state in the proposed systems.