Three-sublattice order in the SU(3) Heisenberg model on the square and triangular lattice

We present a numerical study of the SU (3) Heisenberg model of three-flavor fermions on the triangular and square lattice by means of the density-matrix renormalization group and infinite projected entangled-pair states. For the triangular lattice we confirm that the ground state has a three-sublattice order with a finite ordered moment which is compatible with the result from linear flavor wave theory (LFWT). The same type of order has recently been predicted also for the square lattice T. A. T\'oth et al. , Phys. Rev. Lett. 105, 265301 (2010) from LFWT and exact diagonalization. However, for this case the ordered moment cannot be computed based on LFWT due to divergent fluctuations. Our numerical study clearly supports this three-sublattice order, with an ordered moment of m=0. 2--0. 4 in the thermodynamic limit.