Spin Waves in Finite Spin-½ Heisenberg Chains

Previously unpublished calculations of Carboni and Richards are compared with inelastic—neutron-scattering data in ${\left(\mathrm{C}{\mathrm{H}}_3\right)}_4$ NMn${\mathrm{Cl}}_3$ (TMMC). The calculations, which are exact for frequency and temperature dependence of two spin-correlation functions in spin-½ antiferromagnetic Heisenberg chains containing up to nine spins, show a spin-wave peak at low temperature. The peak broadens and disappears at higher temperatures but does not show an appreciable energy renormalization. These features are consistent with neutron observations of spin waves in TMMC.