Frustration in the anisotropic model on a triangular lattice

We study the X Y antiferromagnet with S = 1 and single-ion anisotropy on a triangular lattice using the bond operator formalism in two cases: the J 1 − J 2 model, which includes a next-nearest-neighbor coupling J 2 , and the spatially-anisotropic J 1 − J 1 ′ model, in which the nearest-neighbor interaction takes a value J 1 ′ along one of the bond directions. The introduction of frustrating second-neighbor interactions leads, at intermediate values of the coupling, to the existence of a disordered phase with the possibility of a quantum liquid behavior. The effect of the frustration on the quantum phase transition is studied. The phase diagrams at T = 0 are presented.