Solution
= Solution
At g=0, $\epsilon_k=2J$ is flat. A domain wall costs 2J, but walls occur in pairs on a periodic spin ring. A single bulk quasiparticle is therefore not automatically the first physical finite-ring spin excitation.
= Solution
At g=0, $\epsilon_k=2J$ is flat. A domain wall costs 2J, but walls occur in pairs on a periodic spin ring. A single bulk quasiparticle is therefore not automatically the first physical finite-ring spin excitation.