Symmetry fractionalization and anomaly detection in three-dimensional topological phases
Abstract
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 andmore »
- Authors:
-
- California Institute of Technology (CalTech), Pasadena, CA (United States)
- Univ. of Colorado, Boulder, CO (United States)
- Publication Date:
- Research Org.:
- Univ. of Colorado, Boulder, CO (United States)
- Sponsoring Org.:
- USDOE Office of Science (SC), Basic Energy Sciences (BES)
- OSTI Identifier:
- 1535793
- Alternate Identifier(s):
- OSTI ID: 1331409
- Grant/Contract Number:
- SC0003910; SC0014415; FG02-10ER46686
- Resource Type:
- Accepted Manuscript
- Journal Name:
- Physical Review B
- Additional Journal Information:
- Journal Volume: 94; Journal Issue: 19; Journal ID: ISSN 2469-9950
- Publisher:
- American Physical Society (APS)
- Country of Publication:
- United States
- Language:
- English
- Subject:
- 75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND SUPERFLUIDITY; Materials Science; Physics; Fractionalization; Gauge theories; Topological phases of matter
Citation Formats
Chen, Xie, and Hermele, Michael. Symmetry fractionalization and anomaly detection in three-dimensional topological phases. United States: N. p., 2016.
Web. doi:10.1103/physrevb.94.195120.
Chen, Xie, & Hermele, Michael. Symmetry fractionalization and anomaly detection in three-dimensional topological phases. United States. https://doi.org/10.1103/physrevb.94.195120
Chen, Xie, and Hermele, Michael. Wed .
"Symmetry fractionalization and anomaly detection in three-dimensional topological phases". United States. https://doi.org/10.1103/physrevb.94.195120. https://www.osti.gov/servlets/purl/1535793.
@article{osti_1535793,
title = {Symmetry fractionalization and anomaly detection in three-dimensional topological phases},
author = {Chen, Xie and Hermele, Michael},
abstractNote = {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.},
doi = {10.1103/physrevb.94.195120},
journal = {Physical Review B},
number = 19,
volume = 94,
place = {United States},
year = {Wed Nov 09 00:00:00 EST 2016},
month = {Wed Nov 09 00:00:00 EST 2016}
}
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