In and around Abelian anyon models

Understand

Anyon models are algebraic structures that model universal topological properties in topological phases of matter and can be regarded as mathematical characterization of topological order in two spacial dimensions.

• It is conjectured that every anyon model, or mathematically unitary modular tensor category, can be realized as the representation category of some chiral conformal field theory, or mathematically vertex operator algebra/local conformal net.
• This conjecture is known to be true for abelian anyon models providing support for the conjecture.
• We reexamine abelian anyon models from several different angles.