Rational $Q$-systems for integrable spin chains without $U(1)$ symmetry
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arXiv
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| Autores principales: | , , , |
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| Formato: | Preprint |
| Publicado: |
2025
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| Acceso en línea: | |
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| _version_ | 1866917116277424128 |
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| author | Jiang, Yunfeng Liu, Yi-Chao Miao, Yuan Tan, Zi-Xi |
| author_facet | Jiang, Yunfeng Liu, Yi-Chao Miao, Yuan Tan, Zi-Xi |
| contents | The $Q$-system is an efficient method for finding complete physical solutions of Bethe ansatz equations, but so far its application has been confined to systems possessing $U(1)$ symmetry. We extend the rational $Q$-system framework to integrable spin chains without $U(1)$ symmetry, exemplified by the closed XXZ model with anti-diagonal twists and the open XXZ model with non-diagonal boundary fields. We demonstrate that the $Q$-system can be derived by combining $TQ$-relation with fusion relations of higher-spin transfer matrices. This yields $QQ$-relations analogous to the $U(1)$ symmetric case but incorporating additional inhomogeneous terms. We present numerical solutions that are validated against exact diagonalization, confirming that it generates all and exclusively physical solutions. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2512_01551 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Rational $Q$-systems for integrable spin chains without $U(1)$ symmetry Jiang, Yunfeng Liu, Yi-Chao Miao, Yuan Tan, Zi-Xi High Energy Physics - Theory The $Q$-system is an efficient method for finding complete physical solutions of Bethe ansatz equations, but so far its application has been confined to systems possessing $U(1)$ symmetry. We extend the rational $Q$-system framework to integrable spin chains without $U(1)$ symmetry, exemplified by the closed XXZ model with anti-diagonal twists and the open XXZ model with non-diagonal boundary fields. We demonstrate that the $Q$-system can be derived by combining $TQ$-relation with fusion relations of higher-spin transfer matrices. This yields $QQ$-relations analogous to the $U(1)$ symmetric case but incorporating additional inhomogeneous terms. We present numerical solutions that are validated against exact diagonalization, confirming that it generates all and exclusively physical solutions. |
| title | Rational $Q$-systems for integrable spin chains without $U(1)$ symmetry |
| topic | High Energy Physics - Theory |
| url | https://arxiv.org/abs/2512.01551 |