Abstract
Symmetry-protected topological (SPT) states are short-range entangled states with symmetry. Nontrivial SPT states have symmetry-protected gapless edge excitations. In 2 dimension (2D), there are an infinite number of nontrivial SPT phases with or symmetry. These phases can be described by or nonlinear-sigma models with a quantized topological term. At an open boundary, the term becomes the Wess-Zumino-Witten term and consequently the boundary excitations are decoupled gapless left movers and right movers. Only the left movers (if ) carry the or quantum numbers. As a result, the SPT phases have a half-integer quantized spin Hall conductance and the SPT phases have an even-integer quantized spin Hall conductance. Both the and SPT phases are symmetric under their subgroup and can be viewed as SPT phases with even-integer quantized Hall conductance.
- Received 1 November 2012
DOI:https://doi.org/10.1103/PhysRevLett.110.067205
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