title: Braiding statistics of loop excitations in three dimensions.
abstract: 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 (Z(N))(K) gauge theories which are obtained by gauging a gapped, short-range entangled lattice boson model with (Z(N))(K) symmetry. We find that different short-range entangled bosonic states with the same (Z(N))(K) symmetry (i.e., different symmetry-protected topological phases) can be distinguished by their three-loop braiding statistics.
authors.affiliation: James Franck Institute and Department of Physics, University of Chicago, Chicago, Illinois 60637, USA.
authors.forename: Chenjie
authors.initials: C
authors.lastname: Wang
authors.affiliation: James Franck Institute and Department of Physics, University of Chicago, Chicago, Illinois 60637, USA.
authors.forename: Michael
authors.initials: M
authors.lastname: Levin