Excitation Spectrum of $S=1$ Antiferromagnetic Chains

Abstract

The dynamical structure factor $S(Q,ω)$ 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 $π\ge \vert Q\vert >0.3π$. At $\vert Q\vert<0.3π$ 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 $Q<0.3π$. 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.