2017/09/30 by Charles Zhaoxi Xiong, A. Alexandradinata · 1 citation
Physics and Astronomy · Mathematics · #cond-mat.str-el #math-ph #math.MP
paper · pdf · doi:10.1103/physrevb.97.115153
published as Phys. Rev. B 97, 115153 (2018) · 27 pages, 14 figs; new in this version: precise fermionic statement of the Hypothesis, arguments for glide-symmetric representative, clarified proofs in Apps. C & E, and title change
arxiv created 2018/03/04 · arxiv updated 2018/03/28
It is demonstrated that fermionic/bosonic symmetry-protected topological (SPT) phases across different dimensions and symmetry classes can be organized using geometric constructions that increase dimensions and symmetry-forgetting maps that change symmetry groups. Specifically, it is shown that the interacting classifications of SPT phases with and without glide symmetry fit into a short exact sequence, so that the classification with glide is constrained to be a direct sum of cyclic groups of order 2 or 4. Applied to fermionic SPT phases in the Wigner-Dyson class AII, this implies that the complete interacting classification in the presence of glide is \mathbb Z4⊕\mathbb Z2⊕\mathbb Z2 in 3 dimensions. In particular, the hourglass-fermion phase recently realized in the band insulator KHgSb must be robust to interactions. Generalizations to spatiotemporal glide symmetries are discussed.