Quantum Monte Carlo study of S=1/2 weakly-anisotropic antiferromagnets on the square lattice

TL;DR

This study uses quantum Monte Carlo simulations to analyze the finite-temperature phase transitions in weakly anisotropic S=1/2 Heisenberg antiferromagnets on a square lattice, revealing that quantum fluctuations do not destroy long-range order even at very small anisotropies.

Contribution

It provides the first detailed quantum Monte Carlo analysis of weakly anisotropic S=1/2 antiferromagnets, demonstrating the persistence of Ising and BKT transitions at minimal anisotropies.

Findings

Ising and BKT universality classes are preserved at anisotropies as small as 10^{-3}

Quantum fluctuations do not eliminate long-range order in the studied models

The results offer a tool for interpreting experimental data on weakly anisotropic two-dimensional antiferromagnets.

Abstract

We study the finite-temperature behaviour of two-dimensional S=1/2 Heisenberg antiferromagnets with very weak easy-axis and easy-plane exchange anisotropies. By means of quantum Monte Carlo simulations, based on the continuous-time loop and worm algorithm, we obtain a rich set of data that allows us to draw conclusions about both the existence and the type of finite-temperature transition expected in the considered models. We observe that the essential features of the Ising universality class, as well as those of the Berezinskii-Kosterlitz-Thouless (BKT) one, are preserved even for anisotropies as small as 10^{-3} times the exchange integral; such outcome, being referred to the most quantum case S=1/2, rules out the possibility for quantum fluctuations to destroy the long or quasi-long range order, whose onset is responsible for the Ising or BKT transition, no matter how small the anisotropy. Besides this general issue, we use our results to extract, out of the isotropic component, the features which are peculiar to weakly anisotropic models, with particular attention for the temperature region immediately above the transition. By this analysis we aim to give a handy tool for understanding the experimental data relative to those real compounds whose anisotropies are too weak for a qualitative description to accomplish the goal of singling out the genuinely two-dimensional critical behaviour.