Reflection positivity and a refined index for 2d invertible phases
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arXiv
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866912733755080704 |
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| author | Sopenko, Nikita |
| author_facet | Sopenko, Nikita |
| contents | We analyze the validity of reflection positivity in the classification of invertible phases of quantum spin systems. We provide a mathematical model in which every 2d invertible state admits a reflection-positive representative. We prove that reflection positivity provides a canonical lift from the set of invertible phases to the set of invertible phases protected by a $\mathbb{Z}/N$-rotational symmetry. Using this, we define a refined version of the index recently introduced by the author. This refined version conjecturally provides a microscopic characterization of an invariant that coincides with the chiral central charge $c_-$ when conformal field theory effectively describes the boundary modes. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2509_01711 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Reflection positivity and a refined index for 2d invertible phases Sopenko, Nikita Mathematical Physics Strongly Correlated Electrons Quantum Physics We analyze the validity of reflection positivity in the classification of invertible phases of quantum spin systems. We provide a mathematical model in which every 2d invertible state admits a reflection-positive representative. We prove that reflection positivity provides a canonical lift from the set of invertible phases to the set of invertible phases protected by a $\mathbb{Z}/N$-rotational symmetry. Using this, we define a refined version of the index recently introduced by the author. This refined version conjecturally provides a microscopic characterization of an invariant that coincides with the chiral central charge $c_-$ when conformal field theory effectively describes the boundary modes. |
| title | Reflection positivity and a refined index for 2d invertible phases |
| topic | Mathematical Physics Strongly Correlated Electrons Quantum Physics |
| url | https://arxiv.org/abs/2509.01711 |