Past exam of the quantum Condensed Matter Field Theory course of the University of Cambridge / 2012 / Paper 1 / 1 / d / i / Solution

At g=0, ${ϵ}_k=2J$ 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.