Anyon

In physics, an anyon is a type of quasiparticle that occurs only in two-dimensional systems, with properties much less restricted than the two kinds of standard elementary particles, fermions and bosons. In general, the operation of exchanging two identical particles, although it may cause a global phase shift, cannot affect observables. Anyons are generally classified as abelian or non-abelian. Abelian anyons (detected by two experiments in 2020) play a major role in the fractional quantum Hall effect. This is an active area of research; using a superconducting processor, Google Quantum AI reported on the first braiding of non-Abelian anyons in an arXiv article by Andersen et al. in October 2022, later published in Nature. In an arXiv article released in May 2023, Quantinuum reported on non-abelian braiding using a trapped-ion processor. The statistical mechanics of large many-body systems obeys laws described by Maxwell–Boltzmann statistics. Quantum statistics is more complicated because of the different behaviors of two different kinds of particles called fermions and bosons. Quoting a recent, simple description:In the three-dimensional world we live in, there are only two types of particles: "fermions," which repel each other, and "bosons," which like to stick together. A commonly known fermion is the electron, which transports electricity; and a commonly known boson is the photon, which carries light. In the two-dimensional world, however, there is another type of particle, the anyon, which doesn't behave like either a fermion or a boson. In a two-dimensional world, two identical anyons change their wavefunction when they swap places in ways that can't happen in three-dimensional physics: in two dimensions, exchanging identical particles twice is not equivalent to leaving them alone. The particles' wavefunction after swapping places twice may differ from the original one; particles with such unusual exchange statistics are known as anyons.