Mixed columnar-plaquette phase of hard-core bosons and its quantum melting

We examine the ground-state phase diagram of repulsively interacting hard-core bosons on the quarter-filled checkerboard lattice using quantum Monte Carlo simulations constrained to the canonical ensemble. At a sufficiently large repulsion, the system undergoes a quantum phase transition from a superfluid into a valence-bond-solid regime. We identify this as a weakly first-order quantum melting transition at quarter filling. Furthermore, by examining appropriate order parameters, we exhibit the mixed nature of the valence bond solid, with both columnar and plaquette long-ranged order. Our results demonstrate the realization of the mixed columnar-plaquette phase found recently for the square lattice quantum dimer model in a microscopic bosonic system.