Absence of local conserved charges of the Fredkin spin chain and its truncated versions
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arXiv
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| Autores principales: | , , , , , |
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| Formato: | Preprint |
| Publicado: |
2025
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| _version_ | 1866917099408982016 |
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| author | Fan, Wen-Ming Hao, Kun Chen, Yang-Yang Zhang, Kun Wang, Xiao-Hui Korepin, Vladimir |
| author_facet | Fan, Wen-Ming Hao, Kun Chen, Yang-Yang Zhang, Kun Wang, Xiao-Hui Korepin, Vladimir |
| contents | Conservation laws serve as the hallmark of integrability. The absence of conserved charges typically implies that the model is nonintegrable. The recently proposed Fredkin spin chain exhibits rich structures, and its ground state is analytically known. However, whether the Fredkin spin chain is integrable remains an open question. In this work, through rigorous analytical calculations, we demonstrate that the Fredkin spin chain, under both periodic and open boundary conditions, lacks local conserved charges, thereby confirming its nonintegrable nature. Furthermore, we find that when one or a portion of the Hamiltonian terms are removed (referred to as the truncated Fredkin spin chain), local conserved charges are still absent. Our findings suggest that in models involving three-site interactions, integrable models are generally rare. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2509_04838 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Absence of local conserved charges of the Fredkin spin chain and its truncated versions Fan, Wen-Ming Hao, Kun Chen, Yang-Yang Zhang, Kun Wang, Xiao-Hui Korepin, Vladimir Quantum Physics Mathematical Physics Exactly Solvable and Integrable Systems Conservation laws serve as the hallmark of integrability. The absence of conserved charges typically implies that the model is nonintegrable. The recently proposed Fredkin spin chain exhibits rich structures, and its ground state is analytically known. However, whether the Fredkin spin chain is integrable remains an open question. In this work, through rigorous analytical calculations, we demonstrate that the Fredkin spin chain, under both periodic and open boundary conditions, lacks local conserved charges, thereby confirming its nonintegrable nature. Furthermore, we find that when one or a portion of the Hamiltonian terms are removed (referred to as the truncated Fredkin spin chain), local conserved charges are still absent. Our findings suggest that in models involving three-site interactions, integrable models are generally rare. |
| title | Absence of local conserved charges of the Fredkin spin chain and its truncated versions |
| topic | Quantum Physics Mathematical Physics Exactly Solvable and Integrable Systems |
| url | https://arxiv.org/abs/2509.04838 |