  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.
