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

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.

21 pages, 26 figures

References in corpus (22)

• Quantum Monte Carlo with Directed Loops
• Stochastic series expansion method with operator-loop update
• Exact, Complete, and Universal Continuous-Time Worldline Monte Carlo Approach to the Statistics of Discrete Quantum Systems
• Cluster Algorithm for Vertex Models
• The Loop Algorithm
• Asymptotic scaling of the square lattice quantum Heisenberg antiferromagnet
• The Square-Lattice Heisenberg Antiferromagnet at Very Large Correlation Lengths
• Exact Quantum Monte Carlo Process for the Statistics of Discrete Systems
• Kosterlitz-Thouless transition of quantum XY model in two dimensions
• Instantaneous Spin Correlations in La2CuO4
• Finite-Size Scaling in Two-Dimensional Superfluids
• Lattice Perturbation Theory for $O(N)$-Symmetric $\sigma$-Models with General Nearest-Neighbour Action I. Conventional Perturbation Theory
• Thermodynamics of isotropic and anisotropic layered magnets: renormalization group approach and 1/N expansion
• The Kosterlitz-Thouless and magnetic transition temperatures in layered magnets with a weak easy-plane anisotropy
• Spin Correlations in the Two-Dimensional Spin-5/2 Heisenberg Antiferromagnet Rb2MnF4
• Reals-space renormalization group study of the anisotropic antiferromagnetic Heisenberg model on the square lattice
• Finite-Size Correlation Length and Violations of Finite-Size Scaling
• Green's Functions from Quantum Cluster Algorithms
• Phase transitions in two-dimensional anisotropic quantum magnets
• Finite-temperature ordering in two-dimensional magnets
• On the evaluation of the specific heat and general off-diagonal n-point correlation functions within the loop algorithm
• Quantum Monte Carlo Study on Magnetization Processes

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