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

In this paper we present a study of the phase diagram and critical properties of the square-lattice quantum XY model, with a single-ion anisotropy and spin S = 1, as a function of the anisotropy parameter D. For D less than a critical value DC, which is the critical point for a quantum phase transition at T = 0, the model presents a Berezinskii–Kosterlitz–Thouless (BKT) transition. This region is adequately described by the self-consistent harmonic approximation. We show that, if we want to use a Schwinger boson theory in this region, we should include fluctuations around the mean-field approximation (which leads to a gauge field) to describe correctly the BKT transition. However both methods are inadequate to describe the large-D phase, and we show that this phase can be studied using the bond operator formalism which gives the correct behaviour for the correlation length as a function of the temperature in the critical point and above. Our results agree with scaling arguments.