Superfluid-Insulator Phase Transitions of the Extended Bose-Hubbard Model

In this paper, the extended Bose-Hubbard model with nearest neighbor interaction is discussed using the method of Green functions in the mean-field approximation. Starting from the two-sublattice approach developed by Hewson and ter Haar, we solve the equations of motion of the Green functions and obtain the energy-band structure. Then, by taking the limit of a vanishing energy gap in the energy-band structure, we find the superfluid-insulator phase boundaries for an integer filling density. Finally, the ground state phase boundaries of the one-dimension extended Bose-Hubbard model for rho = 1 are presented, and the tricritical point is obtained.