Criteria for protected edge modes with Z2 symmetry

@article{Heinrich2018CriteriaFP,
  title={Criteria for protected edge modes with 
Z2
 symmetry},
  author={Chris Heinrich and Michael A. Levin},
  journal={Physical Review B},
  year={2018}
}
We derive a necessary and sufficient criterion for when a two dimensional gapped many-body system with Abelian anyons and a unitary $\mathbb{Z}_2$ symmetry has a protected gapless edge mode. Our criterion is phrased in terms of edge theories --- or more specifically, chiral boson edge theories with $\mathbb{Z}_2$ symmetry --- and it applies to any bosonic or fermionic system whose boundary can be described by such an edge theory. At an operational level, our criterion takes as input a chiral… 

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