Folding approach to topological order enriched by mirror symmetry
Name
PhysRevB.99.085128.pdf
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824.22 KB
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Checksum (MD5)
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Author(s)
Jian, Chao-Ming
Wang, Chenjie
Qi, Yang
Date Issued
February 2019
Journal
Physical Review B
Publisher
American Physical Society
Citation
Qi, Yang, et al. “Folding Approach to Topological Order Enriched by Mirror Symmetry.” Physical Review B, vol. 99, no. 8, Feb. 2019. © 2019 American Physical Society
Version
Final published version
Abstract
We develop a folding approach to study two-dimensional symmetry-enriched topological (SET) phases with the mirror reflection symmetry. Our folding approach significantly transforms the mirror SETs, such that their properties can be conveniently studied through previously known tools: (i) it maps the nonlocal mirror symmetry to an onsite Z[subscript 2] layer-exchange symmetry after folding the SET along the mirror axis, so that we can gauge the symmetry; (ii) it maps all mirror SET information into the boundary properties of the folded system, so that they can be studied by the anyon condensation theory—a general theory for studying gapped boundaries of topological orders; and (iii) it makes the mirror anomalies explicitly exposed in the boundary properties, i.e., strictly 2D SETs and those that can only live on the surface of a 3D system can be easily distinguished through the folding approach. With the folding approach, we derive a set of physical constraints on data that describes mirror SET, namely, mirror permutation and mirror symmetry fractionalization on the anyon excitations in the topological order. We conjecture that these constraints may be complete, in the sense that all solutions are realizable in physical systems. Several examples are discussed to justify this. Previously known general results on the classification and anomalies are also reproduced through our approach.
MIT Department
Massachusetts Institute of Technology. Department of Physics
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DOI of Published Version
https://doi.org/10.1103/PhysRevB.99.085128
