Complete classification of integrability and non-integrability of S=1/2 spin chains with symmetric next-nearest-neighbor interaction
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arXiv
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| Format: | Preprint |
| Publié: |
2025
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| _version_ | 1866911578914291712 |
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| author | Shiraishi, Naoto |
| author_facet | Shiraishi, Naoto |
| contents | We study S=1/2 quantum spin chains with shift-invariant and inversion-symmetric next-nearest-neighbor interaction, also known as zigzag spin chains. We completely classify the integrability and non-integrability of the above class of spin systems. We prove that in this class there are only two integrable models, a classical model and a model solvable by the Bethe ansatz, and all the remaining systems are non-integrable. Our classification theorem confirms that within this class of spin chains, there is no missing integrable model. This theorem also implies the absence of intermediate models with a finite number of local conserved quantities. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2501_15506 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Complete classification of integrability and non-integrability of S=1/2 spin chains with symmetric next-nearest-neighbor interaction Shiraishi, Naoto Statistical Mechanics Strongly Correlated Electrons Mathematical Physics Quantum Physics We study S=1/2 quantum spin chains with shift-invariant and inversion-symmetric next-nearest-neighbor interaction, also known as zigzag spin chains. We completely classify the integrability and non-integrability of the above class of spin systems. We prove that in this class there are only two integrable models, a classical model and a model solvable by the Bethe ansatz, and all the remaining systems are non-integrable. Our classification theorem confirms that within this class of spin chains, there is no missing integrable model. This theorem also implies the absence of intermediate models with a finite number of local conserved quantities. |
| title | Complete classification of integrability and non-integrability of S=1/2 spin chains with symmetric next-nearest-neighbor interaction |
| topic | Statistical Mechanics Strongly Correlated Electrons Mathematical Physics Quantum Physics |
| url | https://arxiv.org/abs/2501.15506 |