TY - JOUR

T1 - Symmetry-protected topological phases, generalized Laughlin argument, and orientifolds

AU - Hsieh, Chang Tse

AU - Sule, Olabode Mayodele

AU - Cho, Gil Young

AU - Ryu, Shinsei

AU - Leigh, Robert G.

N1 - Publisher Copyright:
© 2014 American Physical Society.

PY - 2014/10/27

Y1 - 2014/10/27

N2 - 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.

AB - 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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U2 - 10.1103/PhysRevB.90.165134

DO - 10.1103/PhysRevB.90.165134

M3 - Article

AN - SCOPUS:84908402403

SN - 1098-0121

VL - 90

JO - Physical Review B-Condensed Matter

JF - Physical Review B-Condensed Matter

IS - 16

M1 - 165134

ER -