Superfluid Insulator Transitions of Hard-Core Bosons on the Checkerboard Lattice

We study hard-core bosons on the checkerboard lattice with nearest neighbour 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 four-fold 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 leads us to conclude that the transition {\em 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.