Phase transitions of the frustrated bilayer spin one XY model

In this paper we use the SU(3) Schwinger boson representation, followed by a mean field decoupling, to study the disordered phases of the bilayer spin one quantum XY antiferromagnet on a square lattice with next near neighbor and a single ion anisotropy. The phase diagram at zero temperature is obtained. The ratio η=J⊥/J1 between the interlayer J⊥ to the intralayer near neighbor J1 exchange interactions exhibits a quantum phase transition at a critical ratio ηc=21.725 that separates the small- η Nèel phase from the large η quantum disordered paramagnet. The effect of next near neighbor interactions is discussed. The Neel phase is studied using a self consistent harmonic approximation that takes into account topological effects.