Phase diagram of the half-filled two-dimensional SU(N) Hubbard-Heisenberg model:: A quantum Monte Carlo study -: art. no. 075103

We investigate the phase diagram of the half-filled SU(N) Hubbard-Heisenberg model with hopping t, exchange J, and Hubbard U, on a two-dimensional 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) over right arrow= (pi,pi). Furthermore, low lying spin modes with small spectral weight are apparent around the wave vectors (q) over right arrow=(0,pi) and (q) over right arrow=(pi,0). This gapless spin liquid state is equally found in the SU(4) Heisenberg (U/t ->infinity) 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 24x24.