First-order superfluid-Mott insulator transition of spinor bosons in an   optical lattice
  We study the superfluid-Mott insulator transition of antiferromagnetic spin-1 bosons in an optical lattice described by a Bose-Hubbard model. Our variational study with the Gutzwiller-type trial wave function determines that the superfluid-Mott insulator transition is a first-order one at a part of the phase boundary curve, contrary to the spinless case. This first-order transition may be observed through an experiment, such as a Stern-Gerlach type, under a magnetic field. 
Takashi Kimura, Shunji Tsuchiya, and Susumu Kurihara