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Exotic invertible phases with higher-group symmetries

Hsin, Po-Shen and Ji, Wenjie and Jian, Chao-Ming (2022) Exotic invertible phases with higher-group symmetries. SciPost Physics, 12 . Art. No. 52. ISSN 2542-4653. doi:10.21468/SciPostPhys.12.2.052.

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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 Z₂ 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 Z₂ 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 Z₂ non-anomalous internal higher-form symmetry and time-reversal symmetry.

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Hsin, Po-Shen0000-0002-4764-1476
Additional Information:© 2022 P.-S. Hsin et al. This work is licensed under the Creative Commons Attribution 4.0 International License. Published by the SciPost Foundation. Received 17-09-2021; Accepted 03-01-2022; Published 03-02-2022. We thank Xie Chen, Anton Kapustin, Juven Wang for discussions. We thank Cenke Xu for discussions and participation in the early stage of the project. We thank Meng Cheng and Anton Kapustin for comments on a draft. The work of P.-S. H is supported by the U.S. Department of Energy, Office of Science, Office of High Energy Physics, under Award No. DE-SC0011632, and by the Simons Foundation through the Simons Investigator Award. The work of WJ is supported by NSF Grant No. DMR-1920434, the David and Lucile Packard Foundation, and the Simons Foundation.
Group:Walter Burke Institute for Theoretical Physics
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Department of Energy (DOE)DE-SC0011632
Simons FoundationUNSPECIFIED
David and Lucile Packard FoundationUNSPECIFIED
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Record Number:CaltechAUTHORS:20210629-195551413
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Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:109650
Deposited By: Tony Diaz
Deposited On:29 Jun 2021 22:36
Last Modified:14 Mar 2022 21:09

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