Reconciling the correlation length for high-spin Heisenberg antiferromagnets

TL;DR

This paper confirms that corrected chiral perturbation theory accurately describes the low-temperature spin correlation length in high-spin antiferromagnetic Heisenberg models, validated through extensive quantum Monte Carlo simulations.

Contribution

It provides definitive numerical evidence supporting the field-theoretical description of the AFHM's correlation length for spins S ≥ 1/2, including high-spin cases, with detailed analysis of cutoff effects.

Findings

Confirmation of chiral perturbation theory's accuracy for high-spin AFHM

Numerical results for correlation lengths up to 10^5 lattice spacings

Smooth connection between cutoff effect predictions and other models

Abstract

We present numerical results for the antiferromagnetic Heisenberg model (AFHM) that definitively confirm that chiral perturbation theory, corrected for cutoff effects in the AFHM, leads to a correct field-theoretical description of the low-temperature behavior of the spin correlation length for spins $S \geq 1/2$. With two independent quantum Monte Carlo algorithms and a finite-size-scaling technique, we explore correlation lengths up to $\xi \approx 10^5$ lattice spacings a for spins S=1 and 5/2. We show how the recent prediction of cutoff effects by P. Hasenfratz is approached for moderate $\xi/a={\cal O}(100)$, and smoothly connects with other approaches to modeling the AFHM at smaller correlation lengths.