Exotic invertible phases with higher-group symmetries
Po-Shen Hsin, Wenjie Ji, Chao-Ming Jian
SciPost Phys. 12, 052 (2022) · published 3 February 2022
- doi: 10.21468/SciPostPhys.12.2.052
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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.
Cited by 17
Authors / Affiliations: mappings to Contributors and Organizations
See all Organizations.- 1 Po-Shen Hsin,
- 2 Wenjie Ji,
- 3 Chao-Ming Jian
- 1 Walter Burke Institute for Theoretical Physics
- 2 University of California, Santa Barbara [UCSB]
- 3 Cornell University [CU]