Three-Sublattice Ordering of the SU(3) Heisenberg Model of Three-Flavor Fermions on the Square and Cubic Lattices

Combining a semiclassical analysis with exact diagonalizations, we show that the ground state of the SU(3) Heisenberg model on the square lattice develops three-sublattice long-range order. This surprising pattern for a bipartite lattice with only nearest-neighbor interactions is shown to be the consequence of a subtle quantum order-by-disorder mechanism. By contrast, thermal fluctuations favor two-sublattice configurations via entropic selection. These results are shown to extend to the cubic lattice, and experimental implications for the Mott-insulating states of three-flavor fermionic atoms in optical lattices are discussed.

Figure 1

Sketch of the (a) three-sublattice and (b) two-sublattice phases of the SU(3) antiferromagnetic Heisenberg model.

Figure 2

Flavor-wave dispersions of (a) the three-sublattice state, (b) the helical state with $\cos \theta =0.4$, and (c) the two-sublattice state. (d) Zero-point energy per site, ${\epsilon }_{\mathrm{ZP}}=(1/N_{\Lambda })\sum _{\mathbf{k},\nu }{\omega }_{\nu }(\mathbf{k})/2$, as a function of the wave vector ($q$, $\pm q$) of the helix. The minimum is located at $q=2\pi /3$ in both two and three dimensions.

Figure 3

(a) Energy per site from exact diagonalization of various finite-size square clusters compared to the flavor-wave (FW) result. (b) Tower of states for 18 sites. $\Gamma$ denotes points in the center of the Brillouin zone, with $A1$ and $A2$ one-dimensional and $E1$ two-dimensional IRs, while $W$ is a four-dimensional IR with wave vectors ($\pm 2\pi /3$, $\pm 2\pi /3$).