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Combining a semi-classical analysis with exact diagonalizations, we show thatthe ground state of the SU(3) Heisenberg model on the square lattice developsthree-sublattice long-range order. This surprising pattern for a bipartitelattice with only nearest-neighbor interactions is shown to be the consequenceof a subtle quantum order-by-disorder mechanism. By contrast, thermalfluctuations favor two-sublattice configurations via entropic selection. Theseresults are shown to extend to the cubic lattice, and experimental implicationsfor the Mott-insulating states of three-flavor fermionic atoms in opticallattices are discussed.

Three-sublattice ordering of the SU(3) Heisenberg model of three-flavor fermions on the square and cubic lattices