Quantum Spin Liquid

Frustrated magnets on the kagome lattice — resonating valence bonds, no long-range order, fractionalized excitations

Parameters

Energy: --
|M|: --
Frustration: --
Spin ↑
Spin ↓
Valence bond
H = J₁ Σ⟨i,j⟩ Sᵢ·Sⱼ + J₂ Σ⟪i,j⟫ Sᵢ·Sⱼ  (frustrated Heisenberg)
RVB state: |ψ⟩ = Σ_configs c_p |dimer covering⟩  (Anderson 1973)
Wilson loop: W = ⟨∏ σᵢᶻ⟩ detects Z₂ topological order
Spinon: fractionalized S=½ excitation — no magnon, no coherent quasiparticle