Quantum Monte Carlo simulation of two-dimensional S=1/2 antiferromagnets with very weak easy-plane anisotropy

We study the critical and thermodynamic properties of the S=1/2 two-dimensional quantum XXZ antiferromagnet with weak easy-plane anisotropy making use of the continuous-time Quantum Monte Carlo method based on the loop-cluster algorithm. A detailed finite-size scaling analysis reveals that the model displays a finite temperature Berezinskii-Kosterlitz-Thouless (BKT) transition for anisotropy as small as 10^{-3} the dominant isotropic coupling. For a larger anisotropy (10^{-2}) we single out relevant features of the anisotropic behaviour anticipating the BKT transition. Implications for the experimental observation of a BKT phase in real magnets are discussed.