Frustrated Magnetism: Kagome Flat Band

Geometric frustration prevents long-range order — flat bands host macroscopic degeneracy

Spin Parameters

Observables

⟨E⟩/N:
⟨|m|⟩:
Frustrated bonds: %
Lattice: kagome
The kagome lattice has corner-sharing triangles — every triangle is frustrated under antiferromagnetic coupling (cannot satisfy all 3 bonds). This yields a flat band at energy E=0 in the tight-binding spectrum and a macroscopic ground-state degeneracy ∝ exp(N). Real materials: herbertsmithite ZnCu₃(OH)₆Cl₂, the experimental quantum spin liquid.