We generalize the model of Hatsugai and Kohmoto and find ground states
which do not show the properties of Fermi liquids. We work in two spa
ce dimensions, but it is straightforward to generalize to higher dimen
sions. The ground stale is highly degenerate and then is no discontinu
ity in the momentum distribution: i.e., there is no Fermi, surface. Th
e Green's function generically has a branch cut.