Superfluid insulator transitions of hard-core bosons on the checkerboard lattice

We study hard-core bosons on the checkerboard lattice with nearest-neighbor unfrustrated hopping t and tetrahedral plaquette charging energy U. Analytical arguments and quantum Monte Carlo simulations lead us to the conclusion that the system undergoes a zero temperature (T) quantum phase transition from a superfluid phase at small U/t to a large U/t Mott insulator phase with rho=1/4 for a range of values of the chemical potential mu. Further, the quarter-filled insulator breaks lattice translation symmetry in a characteristic fourfold ordering pattern and occupies a lobe of finite extent in the mu-U/t phase diagram. A quantum Monte Carlo study slightly away from the tip of the lobe provides evidence for a direct weakly first-order superfluid insulator transition away from the tip of the lobe. While analytical arguments lead us to conclude that the transition at the tip of the lobe belongs to a different Landau-forbidden second-order universality class, an extrapolation of our numerical results suggests that the size of the first-order jump does not go to zero even at the tip of the lobe.