Anomalies and symmetry fractionalization in reflection-symmetric topological order

One of the central ideas regarding anomalies in topological phases of matter is that they imply the existence of higher-dimensional physics, with an anomaly in a D-dimensional theory typically being canceled by a bulk (D+1)-dimensional symmetry-protected topological phase (SPT). We demonstrate that...

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Bibliographic Details
Published in:Physical review. B 2016-11, Vol.94 (20), Article 205149
Main Author: Lake, Ethan
Format: Article
Language:English
Subjects:
Anomalies
Quantum numbers
Reflection
Symmetry
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Summary:One of the central ideas regarding anomalies in topological phases of matter is that they imply the existence of higher-dimensional physics, with an anomaly in a D-dimensional theory typically being canceled by a bulk (D+1)-dimensional symmetry-protected topological phase (SPT). We demonstrate that for some topological phases with reflection symmetry, anomalies may actually be canceled by a D-dimensional SPT, provided that it comes embedded in an otherwise trivial (D+1)-dimensional bulk. We illustrate this for the example of ZN topological order enriched with reflection symmetry in (2+1)D, and along the way establish a classification of anomalous reflection symmetry fractionalization patterns. In particular, we show that anomalies occur if and only if both electric and magnetic quasiparticle excitations possess nontrivial fractional reflection quantum numbers.
ISSN:2469-9950
2469-9969
DOI:10.1103/PhysRevB.94.205149