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.Comment: 10 pages, 18 figures, minor changes, two references adde

Superfluid-Insulator transitions of bosons on Kagome lattice at non-integer fillings

We study the superfluid-insulator transitions of bosons on the Kagome lattice at incommensurate filling factors f=1/2 and 2/3 using a duality analysis. We find that at f=1/2 the bosons will always be in a superfluid phase and demonstrate that the T_3 symmetry of the dual (dice) lattice, which results in dynamic localization of vortices due to the Aharanov-Bohm caging effect, is at the heart of this phenomenon. In contrast, for f=2/3, we find that the bosons exhibit a quantum phase transition between superfluid and translational symmetry broken Mott insulating phases. We discuss the possible broken symmetries of the Mott phase and elaborate the theory of such a transition. Finally we map the boson system to a XXZ spin model in a magnetic field and discuss the properties of this spin model using the obtained results.Comment: 10 pages, 8 figures, a few typos correcte