One-dimensional antiferromagnetic spin-wave dispersion
= One-dimensional antiferromagnetic spin-wave dispersion
The nearest-neighbour isotropic chain has linear-spin-wave energy $\omega_k=2JS|\sin k|$ in units $\hbar=a=1$. Gapless points occur at zero and the zone boundary. Integer-spin quantum gaps and strongly fluctuating finite-spin spectra require physics beyond this approximation.