Observability of Bethe-ansatz excitations in Heisenberg-Ising spin systems

The Hohenberg-Brinkman sum rule analysis is extended to Heisenberg-Ising chains of arbitrary anisotropy in uniform magnetic fields. It is found that when the system is gapless, Bethe-ansatz excitations dominate the weight function χzz^''(k,ω) at low k. They do not in general dominate χₓₓ^''. When the excitation spectrum has a small gap, the mean energy of χzz^''(0,ω) is far larger than the gap energy single excitations no longer dominate, although they again become important as the gap gets very large.