Connection between Free-Fermion and Interacting Crystalline Symmetry-Protected Topological Phases
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arXiv
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| Format: | Preprint |
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2024
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| _version_ | 1866912136970633216 |
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| author | Lee, Chen-Shen Shiozaki, Ken Hsieh, Chang-Tse |
| author_facet | Lee, Chen-Shen Shiozaki, Ken Hsieh, Chang-Tse |
| contents | We present a framework for investigating the effects of interactions on crystalline symmetry-protected topological (SPT) phases. Within this framework, one can establish a direct connection between the equivalence classes of free-fermion systems and their corresponding interacting classes. A central component of this framework is the Atiyah-Hirzebruch spectral sequence, which provides a systematic way to represent crystalline SPT phases as SPT phases with internal symmetries on subspaces. We demonstrate the application of this approach through examples in various dimensions: 1d systems with U(1) and reflection symmetry, 2d systems with U(1) and C_{n} rotation symmetry, and 3d systems with U(1) and inversion symmetry. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2411_19287 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Connection between Free-Fermion and Interacting Crystalline Symmetry-Protected Topological Phases Lee, Chen-Shen Shiozaki, Ken Hsieh, Chang-Tse Strongly Correlated Electrons Mesoscale and Nanoscale Physics High Energy Physics - Theory We present a framework for investigating the effects of interactions on crystalline symmetry-protected topological (SPT) phases. Within this framework, one can establish a direct connection between the equivalence classes of free-fermion systems and their corresponding interacting classes. A central component of this framework is the Atiyah-Hirzebruch spectral sequence, which provides a systematic way to represent crystalline SPT phases as SPT phases with internal symmetries on subspaces. We demonstrate the application of this approach through examples in various dimensions: 1d systems with U(1) and reflection symmetry, 2d systems with U(1) and C_{n} rotation symmetry, and 3d systems with U(1) and inversion symmetry. |
| title | Connection between Free-Fermion and Interacting Crystalline Symmetry-Protected Topological Phases |
| topic | Strongly Correlated Electrons Mesoscale and Nanoscale Physics High Energy Physics - Theory |
| url | https://arxiv.org/abs/2411.19287 |