Journal
PHYSICAL REVIEW B
Volume 90, Issue 16, Pages -Publisher
AMER PHYSICAL SOC
DOI: 10.1103/PhysRevB.90.165134
Keywords
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Funding
- ICMT postdoctoral fellowship
- NSF [DMR-1064319]
- Alfred P. Sloan Research Fellowship [FG-BR2014-029]
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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.
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