  We investigate the phase diagram of the half-filled SU(N) Hubbard-Heisenberg
model with hopping t, exchange J and Hubbard U, on a square lattice. In the
large-N limit, and as a function of decreasing values of t/J, the model shows a
transition from a d-density wave state to a spin dimerized insulator. A similar
behavior is observed at N=6 whereas at N=2 a spin density wave insulating
ground state is stabilized. The N=4 model, has a d-density wave ground state at
large values of t/J which as a function of decreasing values of t/J becomes
unstable to an insulating state with no apparent lattice and spin broken
symmetries. In this state, the staggered spin-spin correlations decay as a
power-law,resulting in gapless spin excitations at q = (pi,pi). Furthermore,
low lying spin modes with small spectral weight are apparent around the wave
vectors q = (0,pi) and q = (pi,0). This gapless spin liquid state is equally
found in the SU(4) Heisenberg model in the self-adjoint antisymmetric
representation. An interpretation of this state in terms of a pi-flux phase is
offered. Our results stem from projective (T=0) quantum Monte-Carlo simulations
on lattice sizes ranging up to 24 X 24.
