Symmetry-protected topological phases and orbifolds: Generalized Laughlin's argument

Olabode Mayodele Sule, Xiao Chen, Shinsei Ryu

Research output: Contribution to journalArticlepeer-review

58 Scopus citations


We consider nonchiral symmetry-protected topological phases of matter in two spatial dimensions protected by a discrete symmetry such as ZK or ZK×ZK symmetry. We argue that modular invariance/noninvariance of the partition function of the one-dimensional edge theory can be used to diagnose whether, by adding a suitable potential, the edge theory can be gapped or not without breaking the symmetry. By taking bosonic phases described by Chern-Simons K-matrix theories and fermionic phases relevant to topological superconductors as an example, we demonstrate explicitly that when the modular invariance is achieved, we can construct an interaction potential that is consistent with the symmetry and can completely gap out the edge state.

Original languageEnglish (US)
Article number075125
JournalPhysical Review B - Condensed Matter and Materials Physics
Issue number7
StatePublished - Aug 12 2013
Externally publishedYes

All Science Journal Classification (ASJC) codes

  • Electronic, Optical and Magnetic Materials
  • Condensed Matter Physics


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