title: Fractionalization, topological order, and quasiparticle statistics.
abstract: We argue, based on general principles, that topological order is essential to realize fractionalization in gapped insulating phases in dimensions d > or = 2. In d = 2 with genus g, we derive the existence of the minimum topological degeneracy q(g) if the charge is fractionalized in units of 1/q, irrespective of microscopic model or effective theory. Furthermore, if the quasiparticle is either boson or fermion, it must be at least q(2g).
authors.affiliation: Department of Physics, Tokyo Institute of Technology, Oh-okayama, Meguro-ku, Tokyo 152-8551, Japan.
authors.forename: Masaki
authors.initials: M
authors.lastname: Oshikawa
authors.forename: T
authors.initials: T
authors.lastname: Senthil