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Exotic Invertible Phases with Higher-Group Symmetries

by Po-Shen Hsin, Wenjie Ji, Chao-Ming Jian

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Submission summary

Authors (as registered SciPost users): Po-Shen Hsin · Chao-Ming Jian
Submission information
Preprint Link: scipost_202109_00022v3  (pdf)
Date accepted: 2022-01-03
Date submitted: 2021-12-04 18:27
Submitted by: Hsin, Po-Shen
Submitted to: SciPost Physics
Ontological classification
Academic field: Physics
Specialties:
  • Condensed Matter Physics - Theory
  • High-Energy Physics - Theory
Approach: Theoretical

Abstract

We investigate a family of invertible phases of matter with higher-dimensional exotic excitations in even spacetime dimensions, which includes and generalizes the Kitaev's chain in 1+1d. The excitation has $\mathbb{Z}_2$ higher-form symmetry that mixes with the spacetime Lorentz symmetry to form a higher group spacetime symmetry. We focus on the invertible exotic loop topological phase in 3+1d. This invertible phase is protected by the $\mathbb{Z}_2$ one-form symmetry and the time-reversal symmetry, and has surface thermal Hall conductance not realized in conventional time-reversal symmetric ordinary bosonic systems without local fermion particles and the exotic loops. We describe a UV realization of the invertible exotic loop topological order using the $SO(3)_-$ gauge theory with unit discrete theta parameter, which enjoys the same spacetime two-group symmetry. We discuss several applications including the analogue of ``fermionization'' for ordinary bosonic theories with $\mathbb{Z}_2$ non-anomalous internal higher-form symmetry and time-reversal symmetry.

List of changes

added reference in the last paragraph of Appendix B.

Published as SciPost Phys. 12, 052 (2022)

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