Minimal nonintegrable models with three-site interactions
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arXiv
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| Main Authors: | , , , , |
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| Format: | Preprint |
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2026
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| _version_ | 1866915784584855552 |
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| author | Fan, Wen-Ming Hao, Kun Wang, Xiao-Hui Zhang, Kun Korepin, Vladimir |
| author_facet | Fan, Wen-Ming Hao, Kun Wang, Xiao-Hui Zhang, Kun Korepin, Vladimir |
| contents | A systematic understanding of integrability breaking in translationally invariant spin chains with genuine three-site interactions remains lacking. In this work, we introduce and classify minimal nonintegrable spin-$1/2$ Hamiltonians, defined as models that saturate injectivity while admitting no nontrivial local conserved charges beyond the Hamiltonian. We first rigorously establish the nonintegrability of the deformed Fredkin spin chain with periodic boundary conditions by mapping it to a nearest-neighbor composite-spin representation and excluding all admissible $3$-local conserved charges. Guided by its structure, we then construct five classes of spin-$1/2$ models with genuine three-site interactions. One class is integrable, while the remaining four contain exactly two interaction terms and constitute the minimal nonintegrable three-site models. Our results delineate a sharp boundary between integrability and nonintegrability beyond the nearest-neighbor paradigm. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2602_07867 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Minimal nonintegrable models with three-site interactions Fan, Wen-Ming Hao, Kun Wang, Xiao-Hui Zhang, Kun Korepin, Vladimir Quantum Physics Mathematical Physics Exactly Solvable and Integrable Systems A systematic understanding of integrability breaking in translationally invariant spin chains with genuine three-site interactions remains lacking. In this work, we introduce and classify minimal nonintegrable spin-$1/2$ Hamiltonians, defined as models that saturate injectivity while admitting no nontrivial local conserved charges beyond the Hamiltonian. We first rigorously establish the nonintegrability of the deformed Fredkin spin chain with periodic boundary conditions by mapping it to a nearest-neighbor composite-spin representation and excluding all admissible $3$-local conserved charges. Guided by its structure, we then construct five classes of spin-$1/2$ models with genuine three-site interactions. One class is integrable, while the remaining four contain exactly two interaction terms and constitute the minimal nonintegrable three-site models. Our results delineate a sharp boundary between integrability and nonintegrability beyond the nearest-neighbor paradigm. |
| title | Minimal nonintegrable models with three-site interactions |
| topic | Quantum Physics Mathematical Physics Exactly Solvable and Integrable Systems |
| url | https://arxiv.org/abs/2602.07867 |