Anyons & Braiding
fractional statistics · worldlines · topological phase
Physics: Anyons: particles in 2D with statistics intermediate between bosons and fermions. Exchange phase e^(iθ): θ=0 bosons, θ=π fermions, θ in between → anyons. Unique to 2D: in 3D, exchanging twice = identity → only 0 or π allowed; in 2D, winding matters → braid group (infinite). Abelian anyons: exchange gives only a phase. Non-Abelian anyons: exchange gives matrix — topological gate. Laughlin ν=1/3: charge e/3, statistical angle π/3. Experimental: Bartolomei et al. 2020 confirmed fractional charge e/3; Nakamura et al. 2020 directly measured anyon statistics. SU(2)_k Chern-Simons theory: describes non-Abelian anyons at QHE plateau.