Absence of valence-bond supersolidity on the checkerboard lattice

The stability of the supersolid state of bosons reported recently on the checkerboard lattice in the vicinity of a valence-bond crystal phase is assessed. In contrast to previously identified supersolid phases of lattice bosons, this state would-if stable-provide superfluidity atop a solid with inherent quantum dynamics, restricted to the particular filling fraction of one quarter. Using large-scale quantum Monte Carlo simulations based on the stochastic series expansion method constrained to the canonical ensemble, the supersolid state is, however, found to be unstable in the thermodynamic limit. Converging crossing points in both the winding number fluctuations and the Binder ratio related to the order parameter of the valence-bond crystal instead exhibit a direct quantum melting transition of the crystal into the superfluid regime.