FQHE — Laughlin Quasiparticles & Anyonic Braiding

Fractional statistics: braiding acquires phase eiπ/m — neither boson nor fermion

The FQHE & Anyons

At filling factor ν = 1/m (m odd), electrons form the Laughlin state. Quasihole excitations carry fractional charge e/m and obey fractional statistics.

Ψ_Laughlin ∝ ∏ᵢ﹤ⱼ(zᵢ−zⱼ)ᵐ e^{−Σ|zᵢ|²/4}

When quasiparticle A winds around quasiparticle B, the wavefunction acquires:

Ψ → e^{iπ/m} · Ψ

For m=3 (ν=1/3): phase = π/3 = 60°. This is an anyon — a particle that is neither boson (0) nor fermion (π).

The braiding group (braid group Bₙ) replaces the permutation group. Topological quantum computing would use non-abelian anyons.

Phase: 0°