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. 
Zhi Lin, Jun Zhang, and Ying Jiang
cond-mat.stat-mech