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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.

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