Anyon Condensation and Its Applications

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Bose condensation is central to our understanding of quantum phases of matter. Here, we review Bose condensation in topologically ordered phases (also called topological symmetry breaking), where the condensing bosons have nontrivial mutual statistics with other quasiparticles in the system. We give a nontechnical overview of the relationship between the phases before and after condensation, drawing parallels with more familiar symmetry-breaking transitions. We then review two important applications of this phenomenon. First, we describe the equivalence between such condensation transitions and pairs of phases with gappable boundaries, as well as examples where multiple types of gapped boundary between the same two phases exist. Second, we discuss how such transitions can lead to global symmetries that exchange or permute anyon types. Finally, we discuss the nature of the critical point, which can be mapped to a conventional phase transition in some-but not all-cases.

Original languageEnglish (US)
Pages (from-to)307-327
Number of pages21
JournalAnnual Review of Condensed Matter Physics
StatePublished - Mar 10 2018
Externally publishedYes

Bibliographical note

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© 2018 by Annual Reviews. All rights reserved.


  • Gapless boundary
  • Nonabelian anyons
  • Quantum phase transition
  • Topological order


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