Invertible phases for mixed spatial symmetries and the fermionic crystalline equivalence principle
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arXiv
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| Format: | Preprint |
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2021
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| _version_ | 1866918319805693952 |
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| author | Debray, Arun |
| author_facet | Debray, Arun |
| contents | Freed-Hopkins give a mathematical ansatz for classifying gapped invertible phases of matter with a spatial symmetry in terms of Borel-equivariant generalized homology. We propose a slight generalization of this ansatz to account for cases where the symmetry type mixes nontrivially with the spatial symmetry, such as crystalline phases with spin-1/2 fermions. From this ansatz, we prove as a theorem a "fermionic crystalline equivalence principle," as predicted in the physics literature. Using this and the Adams spectral sequence, we compute classifications of some classes of phases with a point group symmetry; in cases where these phases have been studied by other methods, our results agree with the literature. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2102_02941 |
| institution | arXiv |
| publishDate | 2021 |
| record_format | arxiv |
| spellingShingle | Invertible phases for mixed spatial symmetries and the fermionic crystalline equivalence principle Debray, Arun Mathematical Physics Strongly Correlated Electrons High Energy Physics - Theory Algebraic Topology 81T45 (Primary) 57R90 (Secondary) Freed-Hopkins give a mathematical ansatz for classifying gapped invertible phases of matter with a spatial symmetry in terms of Borel-equivariant generalized homology. We propose a slight generalization of this ansatz to account for cases where the symmetry type mixes nontrivially with the spatial symmetry, such as crystalline phases with spin-1/2 fermions. From this ansatz, we prove as a theorem a "fermionic crystalline equivalence principle," as predicted in the physics literature. Using this and the Adams spectral sequence, we compute classifications of some classes of phases with a point group symmetry; in cases where these phases have been studied by other methods, our results agree with the literature. |
| title | Invertible phases for mixed spatial symmetries and the fermionic crystalline equivalence principle |
| topic | Mathematical Physics Strongly Correlated Electrons High Energy Physics - Theory Algebraic Topology 81T45 (Primary) 57R90 (Secondary) |
| url | https://arxiv.org/abs/2102.02941 |