Phase transitions of the bilayered spin one XY model

The bilayered spin one quantum antiferromagnetic XY model with single ion anisotropy on a square lattice is studied using two different approaches. In the disordered phase we use the SU(3) Schwinger boson representation followed by a mean field decoupling. This technique is appropriate to study disordered phases in the presence of easy plane single ion anisotropy. The phase diagram at zero temperature is obtained. The ratio r =J_T/J between the interlayer J_T to the intralayer J exchange interactions exhibits a quantum phase transition at a critical ratio r_c = 21.725 that separates the small r Neel phase from the large r quantum disordered paramagnet. There are two different ways to destroy the Neel order, by increasing the anisotropy parameter D or increasing the coupling between the layers. We calculate the dispersion relation in the Brillouin zone for some values of D and r, and the gap as a function of r and temperature. The ordered phase is studied using a self consistent harmonic approximation that takes into account topological effects. We calculate the Kosterlitz-Thouless transition temperature as a function of r.