Proof of the absence of local conserved quantities in general spin-1/2 chains with symmetric nearest-neighbor interaction
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arXiv
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| Hauptverfasser: | , , |
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| Format: | Preprint |
| Veröffentlicht: |
2024
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| _version_ | 1866929575114571776 |
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| author | Yamaguchi, Mizuki Chiba, Yuuya Shiraishi, Naoto |
| author_facet | Yamaguchi, Mizuki Chiba, Yuuya Shiraishi, Naoto |
| contents | We provide a rigorous proof of the absence of nontrivial local conserved quantities in all spin-1/2 chains with symmetric nearest-neighbor interaction, except for known integrable systems. This result shows that there are no further integrable system that awaits to be discovered. Our finding also implies that there is no intermediate systems with a finite number of nontrivial local conserved quantities. In addition, we clarify all short-support conserved quantities in non-integrable systems, which we need to take into account in analyses of thermalization and level statistics. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2411_02163 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Proof of the absence of local conserved quantities in general spin-1/2 chains with symmetric nearest-neighbor interaction Yamaguchi, Mizuki Chiba, Yuuya Shiraishi, Naoto Statistical Mechanics Mathematical Physics Quantum Physics We provide a rigorous proof of the absence of nontrivial local conserved quantities in all spin-1/2 chains with symmetric nearest-neighbor interaction, except for known integrable systems. This result shows that there are no further integrable system that awaits to be discovered. Our finding also implies that there is no intermediate systems with a finite number of nontrivial local conserved quantities. In addition, we clarify all short-support conserved quantities in non-integrable systems, which we need to take into account in analyses of thermalization and level statistics. |
| title | Proof of the absence of local conserved quantities in general spin-1/2 chains with symmetric nearest-neighbor interaction |
| topic | Statistical Mechanics Mathematical Physics Quantum Physics |
| url | https://arxiv.org/abs/2411.02163 |