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Rational $Q$-systems for integrable spin chains without $U(1)$ symmetry
by Yunfeng Jiang, Yi-Chao Liu, Yuan Miao, Zi-Xi Tan
Submission summary
| Authors (as registered SciPost users): | Yunfeng Jiang · Yuan Miao |
| Submission information | |
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| Preprint Link: | https://arxiv.org/abs/2512.01551v1 (pdf) |
| Date submitted: | Jan. 12, 2026, 3:18 a.m. |
| Submitted by: | Yunfeng Jiang |
| Submitted to: | SciPost Physics |
| Ontological classification | |
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| Academic field: | Physics |
| Specialties: |
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| Approach: | Theoretical |
Abstract
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.
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