= Easy-plane XXZ antiferromagnetic spin-wave spectrum
{title2=$\epsilon_k=2JS\sqrt{(1-\cos k)(1+\Delta\cos k)}$}
For $0<\Delta<1$, choose a planar Néel reference and rotate local axes to align its longitudinal <spins>. One phase convention gives the displayed full-zone spectrum, linear near $k=0$ with slope $JS\sqrt{2(1+\Delta)}$, and gapped at $k=\pi$ by $2JS\sqrt{2(1-\Delta)}$. Shifting a sublattice phase can interchange the <momentum> locations. Folding the magnetic zone separates the gapless in-plane mode from the gapped out-of-plane polarization. An easy-axis reference in this regime is unstable and does not supply this physical expansion.
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