Exactly solvable quantum spin model via Bethe Ansatz — phases, magnons & entanglement
H = J Σᵢ [SᵢˣSᵢ₊₁ˣ + SᵢʸSᵢ₊₁ʸ + Δ·SᵢᶻSᵢ₊₁ᶻ] − h Σᵢ Sᵢᶻ
Phases (Δ):
Δ < −1: Ferromagnet (↑↑↑↑)
−1 < Δ < 1: Gapless Luttinger liquid
Δ > 1: Antiferromagnet (↑↓↑↓)
Δ = ±1: Critical (SU(2) symmetry)
Bethe Ansatz (1931) gives exact eigenstates as superpositions of magnon scattering states. No mean-field needed.
Top: Spin configuration. Middle: Spin correlations ⟨SᵢᶻSⱼᶻ⟩. Bottom: Magnon density.