Braiding statistics of loop excitations in three dimensions

Chenjie Wang, Michael Levin

Research output: Contribution to journalArticlepeer-review

120 Scopus citations


While it is well known that three dimensional quantum many-body systems can support nontrivial braiding statistics between particlelike and looplike excitations, or between two looplike excitations, we argue that a more fundamental quantity is the statistical phase associated with braiding one loop α around another loop β, while both are linked to a third loop γ. We study this three-loop braiding in the context of (ZN)K gauge theories which are obtained by gauging a gapped, short-range entangled lattice boson model with (ZN)K symmetry. We find that different short-range entangled bosonic states with the same (ZN)K symmetry (i.e., different symmetry-protected topological phases) can be distinguished by their three-loop braiding statistics.

Original languageEnglish
Article number080403
JournalPhysical Review Letters
Issue number8
StatePublished - 19 Aug 2014
Externally publishedYes

ASJC Scopus subject areas

  • Physics and Astronomy (all)


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