Symmetry-protected Topological Phases, Generalized Laughlin Argument and Orientifolds
arXiv:1403.6902 · doi:10.1103/PhysRevB.90.165134
Abstract
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 non-chiral 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.
24 pages
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Cited by in corpus (5)
- Symmetric-Gapped Surface States of Fractional Topological Insulators
- Fermionic Matrix Product States and One-Dimensional Topological Phases
- From orbifolding conformal field theories to gauging topological phases
- Gauging (3+1)-dimensional topological phases: an approach from surface theories
- Stability of Topological Insulators with Non-Abelian Edge Excitations