Kagome Antiferromagnet — Geometric Frustration & Flat Band

The kagome lattice hosts geometric frustration: triangles cannot be simultaneously antiferromagnetically satisfied. This yields a macroscopic ground-state degeneracy, a perfectly flat magnon band at the top of the spectrum, and a spin-liquid ground state without long-range order.

Kagome spins (arrow = spin direction). Color: red/blue frustrated/satisfied bonds.

Magnon dispersion ω(k) along Γ→K→M→Γ. Flat band at ω=2J.

Density of states — delta peak at flat band energy.

Exchange J: 1.0 Next-NN J₂: 0.0 Temperature T: 0.5

Satisfied bonds: —

Frustrated bonds: —

Frustration ratio: —

⟨E⟩/J/N: —

Flat band at ω=2J (always, regardless of k)

Dispersive bands: ω=J±√(4cos²(k·a)+...)