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Braiding Statistics of Loop Excitations in Three Dimensions

Chenjie Wang and Michael Levin
Phys. Rev. Lett. 113, 080403 – Published 19 August 2014
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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.

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  • Received 31 March 2014

DOI:https://doi.org/10.1103/PhysRevLett.113.080403

© 2014 American Physical Society

Authors & Affiliations

Chenjie Wang and Michael Levin

  • James Franck Institute and Department of Physics, University of Chicago, Chicago, Illinois 60637, USA

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Issue

Vol. 113, Iss. 8 — 22 August 2014

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