  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.
