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 (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.
- Publication:
-
Physical Review Letters
- Pub Date:
- August 2014
- DOI:
- 10.1103/PhysRevLett.113.080403
- arXiv:
- arXiv:1403.7437
- Bibcode:
- 2014PhRvL.113h0403W
- Keywords:
-
- 05.30.Pr;
- 03.75.Lm;
- 11.15.Ha;
- Fractional statistics systems;
- Tunneling Josephson effect Bose-Einstein condensates in periodic potentials solitons vortices and topological excitations;
- Lattice gauge theory;
- Condensed Matter - Strongly Correlated Electrons
- E-Print:
- 5+5 pages, 10 figures. Minor changes made to improve clarity, published version