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|Date and time:||21nd Apr. (Thu.) 16:00`|
|Place:||SPring-8, "HOUKOUKAN" seminar room|
|Title:||An additional SU(2) symmetry of the one-dimensional spin-1 biquadratic model with single ion anisotropy|
|uÒ:||Iähá (JAEA, SPring-8j|
|Speaker:||Dr. Keigo Hijii (JAEA, SPring-8)|
Static and dynamical properties of systems are ruled by the symmetry. So making clear the symmetry is important.
A spin-1 one dimensional bilinear-biquadratic model has been an interesting subject from the theoretical point of view. This model with only one parameter has a rich ground state phase diagram. Recently, a possibility of experimental realization of this model in optical lattice systems is proposed . Kolezhuk discussed the ground state of this model with single ion anisotropy (D) using the nonlinear sigma model in some dimensional systems . We have determined this ground state phase diagram by numerical calculations using the levelspectroscopy method and twisted boundary condition . Then we find a phase boundary between the XY2 phase and the Neel phase at θ=-π/2. In D = 0 case, this model with θ=-π/2 has SU(3) symmetry . However, in finite D case, this does not have this SU(3) and standard spin SU(2) symmetry.
We show that the one-dimensional spin-1 biquadratic (BQ) model with single ion anisotropy (θ=-π/2, D:finite) has an additional SU(2) symmetry for periodic, open and twisted boundary conditions.
We can understand degeneracies in our previous numerical results using this symmetry.
 A. Imambekov, M. Lukin, and E. Demler, Phys. Rev. A vol.68, 063602 (2003).
 A. Kolezhuk, Phys. Rev. B vol.78, 144428 (2008).
 K. Takahashi, K. Hijii, and K. Nomura, in preparation.
 I. Affleck, Nucl. Phys. B vol.265, 409 (1986).