Excitation Spectrum of $S=1$ Antiferromagnetic Chains

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 $\pi \ge |Q|>0.3\pi$. At $|Q|<0.3\pi$ 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.

14pages, Revtex 3.0, No.2792

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