semion

A semion is a type of anyon, a quasiparticle that can exist in two-dimensional systems and exhibit fractional statistics that are neither purely bosonic nor fermionic. Semions have a distinctive exchange phase of i, meaning that exchanging two identical semions multiplies the many-body wavefunction by i. Consequently, braiding two semions twice yields a phase of -1, reflecting their nontrivial topological order.

In the simplest theoretical description, the semion model features two particle types: the vacuum and the semion. Fusion rules include s × s = 1, so two semions fuse to the vacuum. The semion carries a topological spin θ that equals e^{iπ/2} = i, distinguishing it from particles with bosonic or fermionic statistics. This framework is often formulated within a topological quantum field theory, such as a U(1)_2 Chern-Simons theory, which captures the essential algebraic data of semionic statistics.

Physically, semions can arise as quasiparticle excitations in certain two-dimensional strongly correlated systems. The most discussed theoretical settings are specific fractional quantum Hall states (notably bosonic Laughlin states at filling factor 1/2) and certain chiral spin liquids, where topological order supports semionic excitations. Experimental confirmation of semionic statistics remains an area of active research, typically pursued through interferometric measurements that probe anyonic braiding phases.

Related concepts include other anyons, both Abelian and non-Abelian, as well as the double semion model, which involves semions of opposite chirality. Semions illustrate how two-dimensional topological phases can host particle statistics beyond the familiar boson–fermion dichotomy.