Spin and quadruple correlations in the insulating nematic phase of spin-1 bosons on optical lattices

Original · EN

We consider the effective model of H=-J₁∑<ᵢ,ⱼ>Sᵢ· Sⱼ-J₂∑<ᵢ,ⱼ>(Sᵢ· Sⱼ) ², describing the Mott insulating phase with odd number of spin-1 bosons in optical lattices (J₂>J₁>0). In terms of an SU(3) boson representation, a valence bond mean field theory is developed. In 1D, a first-order quantum phase transition from a spin singlet to a spin nematic phase with gapful excitations is identified at J₁/J₂=0.19833, while on a 2D square lattice a spin nematic ordered phase with gapless excitations prevails. In both 1D and 2D cases, we predict that the spin structure factor displays dominant antiferromagnetic fluctuations, while the quadrupole structure factor exhibits strong ferroquadrupolar correlations.