不等边Yang-Baxter三元组作为超越普通Yang-Baxter方程的隐藏对称性来源
Scalene Yang--Baxter triples as a source of hidden symmetries beyond the ordinary Yang--Baxter equation
- Indian Institute of Technology Bhubaneswar（印度技术学院布巴内斯瓦尔分校）
- Stony Brook University（石溪大学）
机构由 AI 辅助整理，请以论文原文为准。
AI总结：
该研究以不等边Yang-Baxter三元组为基础构造非厄米自旋链，发现其转移矩阵存在交叉对易性，揭示了普通Yang-Baxter方程框架外的隐藏对称性来源。
AI中文摘要：
我们研究一个由精确非编织不等边Yang-Baxter三元组中的一个成员得到的近邻非厄米自旋链。其局域哈密顿量密度既违反差分形式的Reshetikhin条件，也违反其非差分的一般对应形式，阻碍了它通过普通Yang-Baxter方程的可微齐次正则解实现。由该正则成员构造的转移矩阵在不同谱参数下彼此不对易。不过，不等边Yang-Baxter关系意味着它与由该不等边三元组第三个成员构造的另一个转移矩阵存在交叉对易性。我们对任意链长评估后者，表明在偶周期链上，它是一个非平凡交错幂零对称性的有限生成函数。所得守恒层级完全属于该单一对称性生成的代数，因此不构成代数独立荷的广延族。尽管如此，该示例证明不等边Yang-Baxter三元组可作为超越普通自对易转移矩阵框架的代数对称性发现机制。
英文摘要：
We study a nearest-neighbor non-Hermitian spin chain obtained from one member of an exact non-braided scalene Yang--Baxter triple. Its local Hamiltonian density violates both the difference-form Reshetikhin condition and its general non-difference counterpart, obstructing its realization by a differentiable homogeneous regular solution of the ordinary Yang--Baxter equation. The transfer matrices constructed from the regular member do not commute among themselves at distinct spectral parameters. Nevertheless, the scalene Yang--Baxter relation implies cross-commutativity with another transfer matrix constructed from the third member of the scalene triple. We evaluate the latter for arbitrary chain length and show that, on even periodic chains, it is a finite generating function of a non-obvious staggered nilpotent symmetry. The resulting conserved hierarchy belongs entirely to the algebra generated by this single symmetry and hence does not constitute an extensive family of algebraically independent charges. Nevertheless, this example demonstrates that scalene Yang--Baxter triples can act as an algebraic symmetry-discovery mechanism beyond the ordinary self-commuting transfer-matrix framework.
