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

TL;DR

This paper investigates how tiny easy-plane anisotropies in a 2D S=1/2 Heisenberg antiferromagnet cause a crossover from isotropic to XY behavior, revealing a BKT transition and implications for experiments.

Contribution

It demonstrates the sensitivity of the thermodynamics to small anisotropies and characterizes the crossover and BKT transition in the model using quantum Monte Carlo simulations.

Findings

Crossover between isotropic and planar behavior occurs at a characteristic temperature.

Berezinskii-Kosterlitz-Thouless transition is observed below the crossover.

Experimental detection of non-critical 2D XY behavior is possible within a finite temperature range.

Abstract

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 Sr2CuO2Cl2.