Anyon (experimental: 2020, 2D only)

An anyon is an excitation in two spatial dimensions whose exchange statistics can differ from those of bosons and fermions. Two-dimensional paths can wind around each other in inequivalent ways, so exchanges are described by braids rather than only by permutations.

For Abelian anyons, a braid contributes a phase to the joint quantum state. For non-Abelian anyons, it can act as a noncommuting transformation on an anyon fusion space. Exchange and full encircling must be distinguished: a full braid involves two exchanges in a consistent orientation. In the surface-code anyon model, electric and magnetic excitations are individually bosonic but have mutual encircling phase $-1$, illustrating how mutual statistics can contain information absent from self-statistics. These are collective excitations, not a claim that an ordinary free electron changes its fundamental exchange statistics.