Competition between three-sublattice order and superfluidity in the quantum 3-state Potts model of ultracold bosons and fermions on a square optical lattice

International audienceWe study a quantum version of the three-state Potts model that includes as special cases the effective models of bosons and fermions on the square lattice in the Mott insulating limit. It can be viewed as a model of quantum permutations with amplitudes J_parallel and J_perp for identical and different colors, respectively. For J_parallel=J_perp>0, it is equivalent to the SU(3) Heisenberg model, which describes the Mott insulating phase of 3-color fermions, while the parameter range J_perp0 properties for J_perp0. The transition out of the uniform superfluid (that can be realized with bosons) is shown to be a peculiar type of Kosterlitz-Thouless transition with three types of elementary vortice