The phase diagram and critical properties of the two-dimensional anisotropicXY model

Abstract

In this paper we present a study of the phase diagram and critical properties of the square-lattice quantumXY model, with a single-ion anisotropy and spinS = 1, as a function of theanisotropy parameter D. For D less thana critical value DC, which is the critical point for a quantum phase transition atT = 0, the model presents a Berezinskii–Kosterlitz–Thouless (BKT) transition. This region isadequately described by the self-consistent harmonic approximation. We show that, if wewant to use a Schwinger boson theory in this region, we should include fluctuationsaround the mean-field approximation (which leads to a gauge field) to describecorrectly the BKT transition. However both methods are inadequate to describe thelarge-D phase, and we show that this phase can be studied using the bond operator formalismwhich gives the correct behaviour for the correlation length as a function of thetemperature in the critical point and above. Our results agree with scaling arguments.