Kagome: corner-sharing triangles
Each triangle frustrated → no
Néel order possible
H = J Σ_{⟨ij⟩} S⃗ᵢ·S⃗ⱼ (J > 0)
Classical GS: macroscopically
degenerate; any config with
S_triangle = 0 qualifies
Quantum: RVB (resonating
valence bond) = superposition
of singlet coverings
|ψ_RVB⟩ = Σ_c λ_c |dimer_c⟩
Topological order; Z₂ gauge
theory; spinon & vison excitations
Each triangle frustrated → no
Néel order possible
H = J Σ_{⟨ij⟩} S⃗ᵢ·S⃗ⱼ (J > 0)
Classical GS: macroscopically
degenerate; any config with
S_triangle = 0 qualifies
Quantum: RVB (resonating
valence bond) = superposition
of singlet coverings
|ψ_RVB⟩ = Σ_c λ_c |dimer_c⟩
Topological order; Z₂ gauge
theory; spinon & vison excitations
0.30
0.60
4
ON
⬤ Spin ↑ (blue) / ↓ (red)
═ RVB singlet bond
△ Frustrated (orange)
△ Satisfied (green)