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Generalized homology and Atiyah–Hirzebruch spectral sequence in crystalline symmetry protected topological phenomena

Shiozaki, Ken Xiong, Charles Zhaoxi Gomi, Kiyonori 京都大学 DOI:10.1093/ptep/ptad086

2023.08

概要

We propose that symmetry protected topological (SPT) phases with crystalline symmetry are formulated by equivariant generalized homologies $h^G_n(X)$ over a real space manifold $X$ with $G$ a crystalline symmetry group. The Atiyah-Hirzebruch spectral sequence unifies various notions in crystalline SPT phases such as the layer construction, higher-order SPT phases and Lieb-Schultz-Mattis type theorems. Our formulation is applicable to interacting systems with onsite and crystalline symmetries as well as free fermions.

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© The Author(s) 2023. Published by Oxford University Press on behalf of the Physical Society of Japan. This is an Open Access article distributed under the terms of the Creative Commons

Attribution License (https://cr eativecommons.or g/licenses/by/4.0/), which permits unrestricted reuse, distribution, and reproduction in any medium, provided the original work is properly cited.

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