Spin Waves in Quantum Antiferromagnets

TL;DR

This paper investigates the dispersion of spin waves in quantum antiferromagnets using a mean-field approach and the Mori-Zwanzig projection method, revealing deviations from previous analytic expressions and extending the analysis to arbitrary spins and anisotropies.

Contribution

It provides a systematic analysis of spin wave dispersion in quantum antiferromagnets, showing deviations from earlier formulas and generalizing the method to various spins and anisotropic models.

Findings

Krüger and Schuck's dispersion expression deviates at order 1/Z^2.

The method is extended to arbitrary spin S.

The approach relates to the 1/S expansion and can be improved systematically.

Abstract

Using a self-consistent mean-field theory for the $S=1/2$ Heisenberg antiferromagnet Kr\"uger and Schuck recently derived an analytic expression for the dispersion. It is exact in one dimension ($d=1$) and agrees well with numerical results in $d=2$. With an expansion in powers of the inverse coordination number $1/Z$ ($Z=2d$) we investigate if this expression can be {\em exact} for all $d$. The projection method of Mori-Zwanzig is used for the {\em dynamical} spin susceptibility. We find that the expression of Kr\"uger and Schuck deviates in order $1/Z^2$ from our rigorous result. Our method is generalised to arbitrary spin $S$ and to models with easy-axis anisotropy $\D$. It can be systematically improved to higher orders in $1/Z$. We clarify its relation to the $1/S$ expansion.