An Upper Bound for the Spin-Wave Spectrum of the Heisenberg Antiferromagnet

We study the spin-wave spectrum of the Heisenberg antiferromagnet on a bipartite lattice. The spin-wave spectrum on a N\'eel-ordered ground state is bounded as $\varepsilon (k) \le c |k| $, where $c$ gives an upper bound for the spin-wave velocity. In the large-$S$ limit, the upper bound $c$ coincides with the result of the spin-wave theory.