  An effective action for Bose-Hubbard model with two- and three-body on-site
interaction in a square optical lattice is derived in the frame of a
strong-coupling approach developed by Sengupta and Dupuis. From this effective
action, superfluid-Mott insulator (MI) phase transition, excitation spectrum
and momentum distribution for two phases are calculated by taking into account
Gaussian fluctuation about the saddle-point approximation. In addition the
effects of three-body interaction are also discussed.
