2014/03/31 by Chenjie Wang, Michael Levin · 1 citation
Physics and Astronomy · #cond-mat.str-el
paper · pdf · doi:10.1103/physrevlett.113.080403
published as Phys. Rev. Lett. 113, 080403 (2014) · 5+5 pages, 10 figures. Minor changes made to improve clarity, published version
arxiv created 2014/08/23 · arxiv updated 2014/08/26
While it is well known that three dimensional quantum many-body systems can support non-trivial braiding statistics between particle-like and loop-like excitations, or between two loop-like 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.