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

Abstract : We 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_perp<0. For dominant antiferromagnetic J_parallel interactions, a three-sublattice long-range ordered stripe state is selected out of the ground state manifold of the antiferromagnetic Potts model by quantum fluctuations. Upon increasing |J_perp|, this state is replaced by a uniform superfluid for J_perp<0, and by an exotic three-sublattice superfluid followed by a two-sublattice superfluid for J_perp>0. 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 vortices
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Laura Messio, Philippe Corboz, Frédéric Mila. Competition between three-sublattice order and superfluidity in the quantum 3-state Potts model of ultracold bosons and fermions on a square optical lattice. Physical Review B : Condensed matter and materials physics, American Physical Society, 2013, 88 (15), pp.155106. ⟨10.1103/PhysRevB.88.155106⟩. ⟨cea-01336932⟩

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