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

TL;DR

This paper demonstrates that the SU(3) Heisenberg model on square and cubic lattices exhibits a three-sublattice long-range order due to quantum effects, with implications for cold atom experiments.

Contribution

It reveals a novel three-sublattice ordering in the SU(3) Heisenberg model on bipartite lattices, driven by quantum order-by-disorder mechanisms.

Findings

Ground state shows three-sublattice order on square lattice.

Thermal fluctuations favor two-sublattice configurations.

Results extend to cubic lattices and relate to cold atom experiments.

Abstract

Combining a semi-classical 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.