Valence Bond Solid — Dimerization & AKLT State
Quantum Antiferromagnet · Singlet-Triplet Gap · Haldane Phase
Parameters
Dimerization δ:
1.0
Chain length N:
20
Spin S:
1/2
View mode:
VBS Singlets
AKLT Decomposition
Spectrum / Gap
▶ Animate Dimerization
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.