Temperature dependent correlation length for the S=1/2 Quantum Heisenberg Antiferromagnet on the square lattice

TL;DR

This paper analyzes the temperature dependence of the correlation length in the 2D S=1/2 quantum Heisenberg antiferromagnet using high-precision Monte Carlo simulations, confirming some theoretical predictions at high temperatures but challenging them at low temperatures.

Contribution

It provides high-precision Monte Carlo data for the correlation length across a wide temperature range, testing and challenging existing theoretical predictions.

Findings

Data agrees with theory at high temperatures

Data strongly disagrees with theory at low temperatures

Correlation length reaches up to 95.7(3) in simulations

Abstract

We present an analysis of high precision Monte Carlo data for the two dimensional S=1/2 quantum Heisenberg antiferromagnet up to $\xi = 95.7(3)$ obtained by the continuous time version of the loop algorithm. Our data are in good agreement with a prediction of the recent theory (Phys. Rev. Lett. vol. 77, 3439 (1996)) in very high temperature regime, but they strongly disagree with it in the low temperature regime.