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Title: Symmetry fractionalization and anomaly detection in three-dimensional topological phases

Journal Article · · Physical Review B
 [1];  [2]
  1. California Institute of Technology (CalTech), Pasadena, CA (United States)
  2. Univ. of Colorado, Boulder, CO (United States)
+ Show Author Affiliations

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 3D Z2 gauge theory with Z2 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.

Research Organization:
Univ. of Colorado, Boulder, CO (United States)
Sponsoring Organization:
USDOE Office of Science (SC), Basic Energy Sciences (BES)
Grant/Contract Number:
SC0003910; SC0014415; FG02-10ER46686
OSTI ID:
1535793
Alternate ID(s):
OSTI ID: 1331409
Journal Information:
Physical Review B, Vol. 94, Issue 19; ISSN 2469-9950
Publisher:
American Physical Society (APS)Copyright Statement
Country of Publication:
United States
Language:
English
Citation Metrics:
Cited by: 3 works
Citation information provided by
Web of Science

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Cited By (6)

Fractional S -duality, classification of fractional topological insulators, and surface topological order journal August 2017
Fractional $S$-duality, Classification of Fractional Topological Insulators and Surface Topological Order text January 2017
Time-reversal and spatial reflection symmetry localization anomalies in (2+1)D topological phases of matter text January 2017
Symmetry enriched U(1) quantum spin liquids text January 2017
Bulk characterization of topological crystalline insulators: stability under interactions and relations to symmetry enriched U(1) quantum spin liquids text January 2017
On gapped boundaries for SPT phases beyond group cohomology text January 2019

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Related Subjects

75 CONDENSED MATTER PHYSICS
SUPERCONDUCTIVITY AND SUPERFLUIDITY
Materials Science
Physics
Fractionalization
Gauge theories
Topological phases of matter