Interactions reduce the free-fermion crystalline SPT classification for U(1) with reflection, rotation, or inversion symmetries to finite quotients: Z4 in 1D, Zn-based groups in 2D, and Z8 times Z2 in 3D.
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Connection between Free-Fermion and Interacting Crystalline Symmetry-Protected Topological Phases
Interactions reduce the free-fermion crystalline SPT classification for U(1) with reflection, rotation, or inversion symmetries to finite quotients: Z4 in 1D, Zn-based groups in 2D, and Z8 times Z2 in 3D.