We present a numerical diagonalization study of two one-dimensional
S=21 antiferromagnetic Heisenberg chains, having nearest-neighbor and Haldane-Shastry (
r21) interactions, respectively. We have obtained the
T=0 dynamical correlation function, ${S}^{\ensuremath{\alpha}\ensuremath{\alpha}}(q, \ensuremath{\omega})$, for chains of length $N=8\ensuremath{-}28$. We have studied ${S}^{\mathrm{zz}}(q, \ensuremath{\omega})$ for the Heisenberg chain in zero field, and from finite-size scaling we have obtained a limiting behavior that for large $\ensuremath{\omega}$ deviates from the conjecture proposed earlier by M\"uller et al. For both chains we describe the behavior of ${S}^{\mathrm{zz}}(q, \ensuremath{\omega})$ and ${S}^{\mathrm{xx}}(q, \ensuremath{\omega})$ for selected values of the applied field, and compare with previous work by M\"uller et al. and Talstra and Haldane. Suggestions for future finite-field neutron scattering experiments are made.
We study the Heisenberg spin chain with twisted boundary conditions, focusing on the adiabatic flow of the energy spectrum as a function of the twist angle. In terms of effective field theory for the nearest-neighbor model, we show that the period 2 (in unit
2π) obtained by Sutherland and Shastry arises from irrelevant perturbations around the massless fixed point, and that this period may be rather general for one-dimensional interacting lattice models at half filling. In contrast, the period for the Haldane-Shastry spin model with
1/r2 interaction has a different and unique origin for the period, namely, it reflects fractional statistics in Haldane's sense.