Quantum phase transitions of ultra-cold Bose system in non-rectangular optical lattices

In this paper, we investigate systematically the Mott-insulator-Superfluid quantum phase transitions for ultracold scalar bosons in triangular, hexagonal, as well as Kagom\'e optical lattices. With the help of field-theoretical effective potential, by treating the hopping term in Bose-Hubbard model as perturbation, we calculate the phase boundaries analytically for different integer filling factors. Our analytical results are in good agreement with recent numerical results.