  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/metallic phases under increasing hopping is investigated at T=0K.
More specifically, 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.
