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

Bosonic and fermionic Hubbard models on the checkerboard lattice are studied numerically for infinite on-site repulsion. At particle density n = 1/4 and strong nearest-neighbor repulsion, insulating Valence-Bond crystals (VBC) of resonating particle pairs are stabilized. Their melting into superfluid or metallic phases under increasing hopping is investigated at T = 0 K. We identify a novel and unconventional commensurate VBC supersolid region, precursor to the melting of the bosonic crystal. Hardcore bosons (spins) are compared to fermions (electrons), as well as positive to negative (frustrating) hoppings.