Bosonic and fermionic Hubbard models on the checkerboard lattice are studiednumerically for infinite on-site repulsion. At particle density n=1/4 andstrong nearest-neighbor repulsion, insulating Valence Bond Crystals (VBC) ofresonating particle pairs are stabilized. Their melting intosuperfluid/metallic phases under increasing hopping is investigated at T=0K.More specifically, we identify a novel and unconventional commensurate VBCsupersolid region, precursor to the melting of the bosonic crystal. Hardcorebosons (spins) are compared to fermions (electrons), as well as positive tonegative (frustrating) hoppings.
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