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arXiv · 2512.01551

Rational $Q$-systems for integrable spin chains without $U(1)$ symmetry

Yunfeng Jiang·Yi-Chao Liu·Yuan Miao·Zi-Xi Tan
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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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Yunfeng Jiang, Yi-Chao Liu, Yuan Miao, Zi-Xi Tan. 2025-12-01. Rational $Q$-systems for integrable spin chains without $U(1)$ symmetry. https://doi.org/10.21468/scipostphys.20.6.175

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