Bethe Ansatz equations for XX spin chain with constrained non-diagonal boundaries yield roots of fixed parity at unary-function zeros, with ground-state energy expressed analytically in the thermodynamic limit.
Rational $Q$-systems for integrable spin chains without $U(1)$ symmetry
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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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math-ph 1years
2026 1verdicts
UNVERDICTED 1representative citing papers
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Exact spectrum of the XX spin chain with constrained non-diagonal boundary fields
Bethe Ansatz equations for XX spin chain with constrained non-diagonal boundaries yield roots of fixed parity at unary-function zeros, with ground-state energy expressed analytically in the thermodynamic limit.