Theory of twist liquids: Gauging an anyonic symmetry

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Topological phases in (2+1)-dimensions are frequently equipped with global symmetries, like conjugation, bilayer or electric-magnetic duality, that relabel anyons without affecting the topological structures. Twist defects are static point-like objects that permute the labels of orbiting anyons. Gauging these symmetries by quantizing defects into dynamical excitations leads to a wide class of more exotic topological phases referred as twist liquids, which are generically non-Abelian. We formulate a general gauging framework, characterize the anyon structure of twist liquids and provide solvable lattice models that capture the gauging phase transitions. We explicitly demonstrate the gauging of the Z2-symmetric toric code, SO(2N)1 and SU(3)1 state as well as the S3-symmetric SO(8)1 state and a non-Abelian chiral state we call the "4-Potts" state.

Original languageEnglish (US)
Pages (from-to)349-445
Number of pages97
JournalAnnals of Physics
StatePublished - Sep 1 2015


  • Anyon
  • Topological field theory
  • Topological phases of matter

ASJC Scopus subject areas

  • General Physics and Astronomy


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