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

TL;DR

This paper establishes an upper bound for the spin-wave spectrum of the Heisenberg antiferromagnet on bipartite lattices, aligning with spin-wave theory in the large-spin limit, providing insights into the excitation velocities.

Contribution

It introduces a rigorous upper bound for the spin-wave spectrum of the Heisenberg antiferromagnet, connecting it with spin-wave theory results in the large-S limit.

Findings

The spectrum is bounded by (k) \u2264 c|k|.

The upper bound c matches spin-wave theory in the large-S limit.

Provides a theoretical limit for spin-wave velocities in antiferromagnets.

Abstract

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.