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arXiv · 1810.00801

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

Ken Shiozaki·Charles Zhaoxi Xiong·Kiyonori Gomi
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Abstract

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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Ken Shiozaki, Charles Zhaoxi Xiong, Kiyonori Gomi. 2023-06-22. Generalized homology and Atiyah-Hirzebruch spectral sequence in crystalline symmetry protected topological phenomena. https://doi.org/10.1093/ptep%2Fptad086

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