XXZ Spin Chain — Magnon & Spinon Spectrum
Bethe ansatz exact spectrum: spinon continuum vs magnon branch
Phase: Gapless (Δ=1, XXX point)
The XXZ Heisenberg chain H = J Σ [Sˣᵢ Sˣᵢ₊₁ + Sʸᵢ Sʸᵢ₊₁ + Δ Sᶻᵢ Sᶻᵢ₊₁] − h Σ Sᶻ is exactly solvable via the Bethe ansatz.
At Δ=1 (XXX): gapless spinon continuum (fractionalized S=1/2 excitations). At Δ>1: gapped magnon branch. At Δ<1: XY phase, gapless.
Left: dispersion relation ε(k). Right: dynamical structure factor S(k,ω) as intensity map.