Valence Bond Solid — Dimerization & AKLT State

Quantum Antiferromagnet · Singlet-Triplet Gap · Haldane Phase

Parameters

Energy Spectrum

VBS: Valence bond solid has spins paired into singlets (↑↓−↓↑)/√2 on alternating bonds. Dimerization δ=1 is fully dimerized.

AKLT: Spin-1 chain = two virtual spin-1/2 per site, symmetrized. Edge states are free spin-1/2 — Haldane phase with hidden Z₂×Z₂ symmetry.

Gap: Δ≈0.41J for spin-1 Heisenberg (Haldane gap). VBS gap ∝ δ exactly.