Ising-chain quasiparticle dispersion
= Ising-chain quasiparticle dispersion
{c}
{title2=$\epsilon_k=2J\sqrt{1+g^2-2g\cos k}$}
For nonnegative field $g$, the bulk <quasiparticle> gap is $2J|g-1|$. At $g=0$ the dispersion is flat, $2J$; at large $g$ it is $2Jg-2J\cos k+O(J/g)$. At $g=1$ it becomes $4J|\sin(k/2)|$, linear near the gapless point. The finite periodic spin chain has additional global excitation constraints; a single isolated domain wall is not an allowed closed-chain spin configuration.