Anomalies and symmetry fractionalization in reflection-symmetric topological order

Ethan Lake

doi:10.1103/physrevb.94.205149

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arXiv · 1608.02736

Anomalies and symmetry fractionalization in reflection-symmetric topological order

Ethan Lake

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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 cancelled 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 cancelled 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 $\mathbb{Z}_N$ 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.

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Ethan Lake. 2016-08-09. Anomalies and symmetry fractionalization in reflection-symmetric topological order. https://doi.org/10.1103/physrevb.94.205149

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