Abelian anyon mutual-statistics phase: ψ(a↻b) = exp(2πi·θ)·ψ; Laughlin ν=1/3 gives θ = 1/3 (exp(2πi/3))

Abelian anyon mutual-statistics phase. From framework F7 (braid group π₁), a full braid of particle a around particle b (not an exchange) is represented by a generator of the abelianisation π₁(C_n)^ab → Z. For abelian anyons the…