Vortex-line condensation in three dimensions: A physical mechanism for bosonic topological insulators

Peng Ye Perimeter Institute for Theoretical Physics Zheng-Cheng Gu Perimeter Institute for Theoretical Physics

Publications of CMSA of Harvard mathscidoc:1702.38014

Bosonic topological insulators (BTI) in three dimensions are symmetry-protected topological phases (SPT) protected by time-reversal and boson number conservation symmetries. BTI in three dimensions were first proposed and classified by the group cohomology theory which suggests two distinct root states, each carrying a Z2 index. Soon after, surface anomalous topological orders were proposed to identify different root states of BTI, which even leads to a new BTI root state beyond the group cohomology classification. In this paper, we propose a universal physical mechanism via vortex-line condensation from a 3d superfluid to achieve all three root states. It naturally produces bulk topological quantum field theory (TQFT) description for each root state. Topologically ordered states on the surface are rigorously derived by placing TQFT on an open manifold, which allows us to explicitly demonstrate the bulk-boundary correspondence. Finally, we generalize the mechanism to ZN symmetries and discuss potential SPT phases beyond the group cohomology classification.
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@inproceedings{pengvortex-line,
  title={Vortex-line condensation in three dimensions: A physical mechanism for bosonic topological insulators},
  author={Peng Ye, and Zheng-Cheng Gu},
  url={http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20170207001301310258214},
}
Peng Ye, and Zheng-Cheng Gu. Vortex-line condensation in three dimensions: A physical mechanism for bosonic topological insulators. http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20170207001301310258214.
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