The zero-temperature phase diagram of the checkerboard Hubbard model is obtained in the solvable limit in which it consists of weakly coupled square plaquettes. As a function of the on-site Coulomb repulsion U and the density of holes per site, x, we demonstrate the existence of at least 16 distinct phases. For instance, at zero doping, the ground state is a novel d-wave Mott insulator (d-Mott), which is not adiabatically continuable to a band insulator; by doping the d-Mott state with holes, depending on the magnitude of U, it gives way to a d-wave superconducting state, a two-flavor spin-$1∕2$ Fermi liquid (FL), or a spin-$3∕2$ FL.
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Yao et al. (2007) studied this question.