Quantum Melting of Valence Bond Crystal Insulators and Novel Supersolid Phase at Commensurate Density

4 pages, 5 figures.International audienceBosonic and fermionic Hubbard models on the checkerboard lattice are studied in the large-U limit by numerical techniques. At fractional particle density n=1/4 and strong nearest-neighbor repulsion, insulating spatially-anisotropic Valence Bond Crystals (VBC) are stabilized. Melting of these bosonic/fermionic crystals under increasing hopping is investigated at T=0K showing unconventional phase transitions towards superfluid/metallic phases. More specifically, we provide evidence for a novel commensurate VBC supersolid region, precursor to the melting of the bosonic crystal. Comparisons between (hardcore) bosons and (spinful) fermions as well as between positive or negative hoppings (frustration) are considered