Exotic Invertible Phases with Higher-Group Symmetries

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.

62 pages, 4 figures, 3 tables; v2: typos corrected, added discussion about gapped and unique ground state

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Cited by in corpus (1)

• Lattice construction of exotic invertible topological phases