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

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 disc...

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Bibliographic Details
Published in:Physical review. B, Condensed matter and materials physics Condensed matter and materials physics, 2014-10, Vol.90 (16), Article 165134
Main Authors: Hsieh, Chang-Tse, Sule, Olabode Mayodele, Cho, Gil Young, Ryu, Shinsei, Leigh, Robert G.
Format: Article
Language:English
Subjects:
Condensed matter
Field theory
Insertion
Parity
Phases
Stability
Symmetry
Theorems
Topology
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Summary: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 CRT 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.
ISSN:1098-0121
1550-235X
DOI:10.1103/PhysRevB.90.165134