The Square-Lattice Heisenberg Antiferromagnet at Very Large Correlation Lengths

TL;DR

This paper introduces a novel computational approach combining a loop cluster algorithm with finite-size scaling to measure extremely large correlation lengths in the square-lattice spin-1/2 Heisenberg antiferromagnet, resolving previous uncertainties.

Contribution

It presents a new method that allows probing correlation lengths up to 350,000 lattice spacings, vastly exceeding previous capabilities, and clarifies the applicability of asymptotic-scaling formulas.

Findings

Measured correlation lengths up to 350,000 lattice spacings.

Resolved the applicability of asymptotic-scaling formulas.

Provided precise low-energy observable values.

Abstract

The correlation length of the square-lattice spin-1/2 Heisenberg antiferromagnet is studied in the low-temperature (asymptotic-scaling) regime. Our novel approach combines a very efficient loop cluster algorithm -- operating directly in the Euclidean time continuum -- with finite-size scaling. This enables us to probe correlation lengths up to $\xi \approx 350,000$ lattice spacings -- more than three orders of magnitude larger than any previous study. We resolve a conundrum concerning the applicability of asymptotic-scaling formulae to experimentally- and numerically-determined correlation lengths, and arrive at a very precise determination of the low-energy observables. Our results have direct implications for the zero-temperature behavior of spin-1/2 ladders.