| 要旨 |
In this talk, I first give a brief review on the superfluid-Mott insulating phase transition of
ultracold boson atoms in optical lattices, and then focu s on the effective model in the Mott insulating
phase with odd number of spin-1 bosons.
In terms of an SU(3) boson representation, a valence bond mean f ield theory is developed.
In 1D, a first-order quantum phase transition from a spin singlet to a quadrupole phase with gapful
excitations is identified, while on a 2D square lattice a quadrupolar ordering phase with gapless excit ations
always prevails. In both 1D and 2D cases, we find that the spin struc ture factor displays dominant
antiferromagnetic fluctuations, while the quad rupolar structure factor exhibits strong ferroquadrupolar
correlations.
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