Phase diagram of dipolar hard-core bosons on honeycomb lattice
  In this paper, we study phase diagrams of dipolar hard-core boson gases on the honeycomb lattice. The system is described by the Haldane-Bose-Hubbard model with complex hopping amplitudes and the nearest neighbor repulsion. By using the slave-particle representation of the hard-core bosons and also the path-integral quantum Monte-Carlo simulations, we investigate the system and to show that the systems have a rich phase diagram. There are Mott, superfluid, chiral superfluid, and sublattice chiral superfluid phases as well as the density-wave phase. We also found that there exists a coexisting phase of superfluid and chiral superfluid. Critical behaviors of the phase transitions are also clarified. 
Takashi Nakafuji, Takeshi Ito, Yuya Nagamori, Ikuo Ichinose
cond-mat.quant-gas