Exotic invertible phases with higher-group symmetries

Journal Article · 02 February 2022 · SciPost Physics

DOI: https://doi.org/10.21468/SciPostPhys.12.2.052 · OSTI ID:1843512

Hsin, Po-Shen ^[1]; Ji, Wenjie ^[2]; Jian, Chao-Ming ^[3]

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1. Walter Burke Institute for Theoretical Physics
2. University of California, Santa Barbara
3. Cornell University

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 ${\mathbb{Z}}_2$ 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 ${\mathbb{Z}}_2$ 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)_- $SO(3{)}_{-}$ 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 ${\mathbb{Z}}_2$ non-anomalous internal higher-form symmetry and time-reversal symmetry.

• Sponsoring Organization: USDOE
• Grant/Contract Number: SC0011632
• OSTI ID: 1843512
• Journal Information: SciPost Physics, Journal Name: SciPost Physics Journal Issue: 2 Vol. 12; ISSN 2542-4653
• Publisher: Stichting SciPostCopyright Statement
• Country of Publication: Netherlands
• Language: English