Symmetry-protected topological phases, generalized Laughlin argument, and orientifolds

Chang Tse Hsieh, Olabode Mayodele Sule, Gil Young Cho, Shinsei Ryu, Robert G. Leigh

Research output: Contribution to journalArticlepeer-review

49 Scopus citations


We generalize Laughlin's flux insertion argument, originally discussed in the context of the quantum Hall effect, to topological phases protected by non-on-site unitary symmetries, in particular by parity symmetry or parity symmetry combined with an on-site unitary symmetry. As a model, we discuss fermionic or bosonic systems in two spatial dimensions with CP symmetry, which are, by the CPT theorem, related to time-reversal symmetric topological insulators (e.g., the quantum spin Hall effect). In particular, we develop the stability/instability (or "gappability"/"ingappablity") criteria for nonchiral conformal field theories with parity symmetry that may emerge as an edge state of a symmetry-protected topological phase. A necessary ingredient, as it turns out, is to consider the edge conformal field theories on unoriented surfaces, such as the Klein bottle, which arises naturally from enforcing parity symmetry by a projection operation.

Original languageEnglish (US)
Article number165134
JournalPhysical Review B - Condensed Matter and Materials Physics
Issue number16
StatePublished - Oct 27 2014
Externally publishedYes

All Science Journal Classification (ASJC) codes

  • Electronic, Optical and Magnetic Materials
  • Condensed Matter Physics


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