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The Square-Lattice Heisenberg Antiferromagnet at Very Large Correlation Lengths

B. B. Beard·R. J. Birgeneau·M. Greven·U. -J. Wiese
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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 $ξ\approx 350,000$ 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.

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B. B. Beard, R. J. Birgeneau, M. Greven, U. -J. Wiese. 1997-12-23. The Square-Lattice Heisenberg Antiferromagnet at Very Large Correlation Lengths. https://doi.org/10.1103/physrevlett.80.1742

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