Abstract 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 ⊥ / J 1 between the interlayer J ⊥ to the intralayer near neighbor J1 exchange interactions exhibits a quantum phase transition at a critical ratio η c = 21.725 that separates the small- η Neel 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.

中文翻译：

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受挫双层自旋一 XY 模型的相变

摘要 在本文中，我们使用 SU(3) Schwinger 玻色子表示，然后是平均场解耦，来研究具有下近邻和单离子各向异性的方形晶格上双层自旋一量子 XY 反铁磁体的无序相。得到零温相图。层间 J ⊥ 与层内近邻 J1 交换相互作用之间的比率 η = J ⊥ / J 1 表现出临界比率 η c = 21.725 的量子相变，它将小 η Neel 相与大 η 量子无序顺磁体分开. 讨论了下一个近邻相互作用的影响。使用考虑拓扑效应的自洽谐波近似来研究尼尔相位。