Complete Classification of Integrability and Non-integrability for Spin-1/2 Chain with Symmetric Nearest-Neighbor Interaction
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arXiv
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| Auteurs principaux: | , , |
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| Format: | Preprint |
| Publié: |
2024
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| _version_ | 1866912104556003328 |
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| author | Yamaguchi, Mizuki Chiba, Yuuya Shiraishi, Naoto |
| author_facet | Yamaguchi, Mizuki Chiba, Yuuya Shiraishi, Naoto |
| contents | General spin-1/2 chains with symmetric nearest-neighbor interaction are studied. We rigorously prove that all spin models in this class, except for known integrable systems, are non-integrable in the sense that they possess no nontrivial local conserved quantities. This result confirms that there are no missing integrable systems, i.e., integrable systems in this class are exactly those that are already known. In addition, this result excludes the possibility of intermediate systems which have a finite number of nontrivial local conserved quantities. Our findings support the expectation that integrable systems are exceptional in quantum many-body systems and most systems are non-integrable. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2411_02162 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Complete Classification of Integrability and Non-integrability for Spin-1/2 Chain with Symmetric Nearest-Neighbor Interaction Yamaguchi, Mizuki Chiba, Yuuya Shiraishi, Naoto Statistical Mechanics Mathematical Physics Quantum Physics General spin-1/2 chains with symmetric nearest-neighbor interaction are studied. We rigorously prove that all spin models in this class, except for known integrable systems, are non-integrable in the sense that they possess no nontrivial local conserved quantities. This result confirms that there are no missing integrable systems, i.e., integrable systems in this class are exactly those that are already known. In addition, this result excludes the possibility of intermediate systems which have a finite number of nontrivial local conserved quantities. Our findings support the expectation that integrable systems are exceptional in quantum many-body systems and most systems are non-integrable. |
| title | Complete Classification of Integrability and Non-integrability for Spin-1/2 Chain with Symmetric Nearest-Neighbor Interaction |
| topic | Statistical Mechanics Mathematical Physics Quantum Physics |
| url | https://arxiv.org/abs/2411.02162 |