Excitation Spectrum of $S=1$ Antiferromagnetic Chains

TL;DR

This paper calculates the dynamical structure factor of a finite $S=1$ antiferromagnetic Heisenberg chain at zero temperature, explaining the absence of clear peaks at certain momentum regions and contrasting with $S=1/2$ chains.

Contribution

It provides detailed numerical analysis of the excitation spectrum of $S=1$ chains, clarifying the nature of low-energy states and their experimental signatures.

Findings

Lowest energy states form delta-function peaks near $Q=\pi$

No clear peaks observed at $Q<0.3\pi$ due to continuum edge dominance

Contrasts with $S=1/2$ chains where lowest states are always continuum edges

Abstract

The dynamical structure factor $S(Q,\omega)$ of the $S=1$ antiferromagnetic Heisenberg chain with length 20 at zero temperature is calculated. The lowest energy states have the delta-function peak at the region $\pi\ge \vert Q\vert >0.3\pi$. At $\vert Q\vert<0.3\pi$ the lowest energy states are the lower-edge of the continuum of the scattering state, the strength of which decreases for large systems. This gives a reasonable explanation for the experimental fact that no clear peak is observed at the region $Q<0.3\pi$. This situation is more apparent for valence-bond solid state. On the contrary for $S=1/2$ antiferromagnetic Heisenberg chain the lowest energy states are always the edge of the continuum.