Spin Waves in Antiferromagnetic Spin Chains with Long Range Interactions

TL;DR

This paper investigates the stability of antiferromagnetic Neel order in long-range interacting spin chains using spin wave theory, revealing conditions under which order persists and analyzing the excitation spectrum.

Contribution

It provides a detailed analysis of Neel order stability in long-range antiferromagnetic chains, including critical exponents and the behavior of spin wave spectra.

Findings

Neel order is stable at T=0 for decay exponent β<3.

Neel order survives up to finite temperature for β<2.

Spin wave spectra are gapless with non-linear momentum dependence.

Abstract

We study antiferromagnetic spin chains with unfrustrated long-range interactions that decays as a power law with exponent $\beta$, using the spin wave approximation. We find for sufficiently large spin $S$, the Neel order is stable at T=0 for $\beta < 3$, and survive up to a finite Neel temperature for $\beta < 2$, validating the spin-wave approach in these regimes. We estimate the critical values of $S$ and $T$ for the Neel order to be stable. The spin wave spectra are found to be gapless but have non-linear momentum dependence at long wave length, which is responsible for the suppression of quantum and thermal fluctuations and stabilizing the Neel state. We also show that for $\beta\le 1$ and for a large but finite-size system size $L$, the excitation gap of the system approaches zero slower than $L^{-1}$, a behavior that is in contrast to the Lieb-Schulz-Mattis theorem.