Anyon

Summary

An anyon is a particle, or quasiparticle, in a two-dimensional system whose exchange statistics is neither bosonic nor fermionic. Exchanging two identical anyons can multiply the state by any phase $e^{i\theta}$, or even act by a non-commuting matrix. This is possible because in the plane the paths that swap particles form the braid group, rather than the symmetric group. Anyons appear as excitations in the fractional quantum Hall effect, and non-abelian anyons are a proposed basis for topological quantum computation.