Asymptotic Freedom and Large Spin Antiferromagnetic Chains

TL;DR

This paper analyzes large-spin antiferromagnetic chains using the nonlinear sigma model, deriving analytic spin correlation expressions valid at specific scales, and validates results with quantum Monte Carlo simulations.

Contribution

It provides new analytic expressions for spin correlations in large-$S$ chains based on the nonlinear sigma model and confirms their accuracy through numerical simulations.

Findings

Analytic spin correlation expressions valid at certain scales

Confirmation of theoretical predictions with Monte Carlo data for S=5/2

Demonstration of asymptotic freedom in large-$S$ spin chains

Abstract

Building on the mapping of large-$S$ spin chains onto the O($3$) nonlinear $\sigma$ model with coupling constant $2/S$, and on general properties of that model (asymptotic freedom, implying that perturbation theory is valid at high energy, and Elitzur's conjecture that rotationally invariant quantities are infrared finite in perturbation theory), we use the Holstein-Primakoff representation to derive analytic expressions for the equal-time and dynamical spin-spin correlations valid at distances smaller than $S^{-1} \exp(\pi S)$ or at energies larger than $J S^2 \exp(-\pi S)$, where $J$ is the Heisenberg exchange coupling. This is supported by comparing the static correlations with quantum Monte Carlo simulations for $S = 5/2$.