Detection of XY behaviour in weakly anisotropic quantum antiferromagnets on the square lattice

We consider the Heisenberg antiferromagnet on the square lattice with S=1/2 and very weak easy-plane exchange anisotropy; by means of the quantum Monte Carlo method, based on the continuous-time loop algorithm, we find that the thermodynamics of the model is highly sensitive to the presence of tiny anisotropies and is characterized by a crossover between isotropic and planar behaviour. We discuss the mechanism underlying the crossover phenomenon and show that it occurs at a temperature which is characteristic of the model. The expected Berezinskii-Kosterlitz-Thouless transition is observed below the crossover: a finite range of temperatures consequently opens for experimental detection of non-critical 2D XY behaviour. Direct comparison is made with uniform susceptibility data relative to the S=1/2 layered antiferromagnet Sr_2CuO_2Cl_2.