1. Anomalies and symmetry fractionalization in reflection-symmetric topological order.
- Author
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Lake, Ethan
- Subjects
- *
TOPOLOGY , *QUASIPARTICLES , *QUANTUM numbers , *MATHEMATICAL physics - Abstract
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. [ABSTRACT FROM AUTHOR]
- Published
- 2016
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