Phase diagram of the SU(N) Hubbard-Heisenberg model on the honeycomb lattice

We present a projective ${T=0}$ quantum Monte-Carlo study of the ground-state properties of the the SU($N$) Hubbard Heisenberg model on hexagonal lattices up to ${18 \times 18}$ unit cells. The phase diagram is mapped out for increasing many body correlations from the large-$N$ limit to SU(2) for even $N$. It is shown that for all SU($N$) symmetric realizations, the model undergoes a quantum phase transition from a semimetal to an insulator for large values of $J/t$. While for ${N \ge 4}$ the insulating state is a valence bond crystal the SU(2) Hubbard Heisenberg model exhibits a gapped short range resonating valence bond phase separating the semimetal and an antiferromagnetic insulator. At SU(2) we reproduce the intermediate spin liquid phase found recently in the SU(2) Hubbard model on the hexagonal lattice.