Simple Exactly Solvable Models of non-Fermi Liquids

We generalize the model of Hatsugai and Kohmoto [J. Phys. Soc. Jpn, 61, 2056 (1992)] and find ground states which do not show the properties of Fermi liquids. We work in two space dimensions, but it is straightforward to generalize to higher dimensions. The ground state is highly degenerate and there is no discontinuity in the momentum distribution; i.e., there is no Fermi surface. The Green's function generically has a branch cut.