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Symmetry fractionalization and anomaly detection in three-dimensional topological phases

Chen, Xie and Hermele, Michael (2016) Symmetry fractionalization and anomaly detection in three-dimensional topological phases. Physical Review B, 94 (19). Art. No. 195120. ISSN 1098-0121. doi:10.1103/PhysRevB.94.195120.

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In a phase with fractional excitations, topological properties are enriched in the presence of global symmetry. In particular, fractional excitations can transform under symmetry in a fractionalized manner, resulting in different symmetry enriched topological (SET) phases. While a good deal is now understood in 2D regarding what symmetry fractionalization patterns are possible, the situation in 3D is much more open. A new feature in 3D is the existence of loop excitations, so to study 3D SET phases, first we need to understand how to properly describe the fractionalized action of symmetry on loops. Using a dimensional reduction procedure, we show that these loop excitations exist as the boundary between two 2D SET phases, and the symmetry action is characterized by the corresponding difference in SET orders. Moreover, similar to the 2D case, we find that some seemingly possible symmetry fractionalization patterns are actually anomalous and cannot be realized strictly in 3D. We detect such anomalies using the flux fusion method we introduced previously in 2D. To illustrate these ideas, we use the 3DZ_2 gauge theory with Z_2 global symmetry as an example, and enumerate and describe the corresponding SET phases. In particular, we find four nonanomalous SET phases and one anomalous SET phase, which we show can be realized as the surface of a 4D system with symmetry protected topological order.

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Additional Information:© 2016 American Physical Society. Received 8 April 2016; revised manuscript received 8 October 2016; published 9 November 2016. X.C. would like to acknowledge discussions with Meng Cheng, Ashvin Vishwanath, Michael Levin and Chenjie Wang, Beni Yoshida, and Aleksander Kubica. X.C. is supported by the Caltech Institute for Quantum Information and Matter and the Walter Burke Institute for Theoretical Physics. M.H. is supported by the US Department of Energy, Office of Science, Basic Energy Sciences, under Award No. DE-FG02-10ER46686 (April 2015 and earlier) and under Award No. DE-SC0014415 (August 2015 and later), and by Simons Foundation Grant No. 305008 (sabbatical support).
Group:Institute for Quantum Information and Matter, Walter Burke Institute for Theoretical Physics
Funding AgencyGrant Number
Institute for Quantum Information and Matter (IQIM)UNSPECIFIED
Walter Burke Institute for Theoretical Physics, CaltechUNSPECIFIED
Department of Energy (DOE)DE-FG02-10ER46686
Department of Energy (DOE)DE-SC0014415
Simons Foundation305008
Issue or Number:19
Record Number:CaltechAUTHORS:20160510-094301838
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Official Citation:Symmetry fractionalization and anomaly detection in three-dimensional topological phases Xie Chen and Michael Hermele Phys. Rev. B 94, 195120
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:66866
Deposited By: Ruth Sustaita
Deposited On:10 May 2016 19:15
Last Modified:11 Nov 2021 00:23

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