Bose-Hubbard model on a star lattice

We analyze the Bose-Hubbard model of hardcore bosons with nearest neighbor hopping and repulsive interactions on a star lattice using both quantum Monte Carlo simulation and dual vortex theory. We obtain the phase diagram of this model as a function of the chemical potential and the relative strength of hopping and interaction. In the strong interaction regime, we find that the Mott phases of the model at 1/2 and 1/3 fillings, in contrast to their counterparts on square, triangular, and Kagome lattices, are either translationally invariant resonant valence bond (RVB) phases with no density-wave order or have coexisting density-wave and RVB orders. We also find that upon increasing the relative strength of hopping and interaction, the translationally invariant Mott states undergo direct second order superfluid-insulator quantum phase transitions. We compute the critical exponents for these transitions and argue using the dual vortex picture that the transitions, when approached through the tip of the Mott lobe, belong to the inverted XY universality class.