AI 中文总结
该研究证明了广泛标准场景下Reshetikhin条件是Yang–Baxter可积性的充要条件，建立了其与局域守恒量的关联，简化了可积自旋链的寻找工作。
AI 中文摘要
量子可积性是相互作用量子自旋链精确理论的基石。然而在标准表述中，人们从满足Yang–Baxter方程的R矩阵出发，而非从哈密顿量本身出发，因此长期以来尚不清楚如何直接在哈密顿量层面刻画Yang–Baxter可解性，以及其与局域守恒量的存在性有何关联。在此，我们证明在广泛的标准场景下，Reshetikhin条件不仅是Yang–Baxter可积性的必要条件，也是充分条件，从而将可积性的隐藏代数结构简化为哈密顿量层面的守恒定律。由于Reshetikhin条件等价于总能量流的守恒，这一哈密顿量层面的判据也具有实验可及性。该结果为各向同性自旋链建立了Liouville–Arnold定理的量子对应，即Yang–Baxter可解性等价于无穷多局域守恒量的层级。我们的结果还通过将对R矩阵的搜索替换为对局域哈密顿量的直接判据，大幅简化了可积自旋链的寻找工作。
英文摘要
Quantum integrability is a cornerstone of the exact theory of interacting quantum spin chains. In its standard formulation, however, one starts from R-matrices satisfying the Yang--Baxter equation, rather than from the Hamiltonian itself. It has therefore remained unclear how Yang--Baxter solvability can be characterized directly at the Hamiltonian level, and how it is related to the existence of local conservation laws. Here we prove that, in a broad standard setting, the Reshetikhin condition is not only necessary but also sufficient for Yang--Baxter integrability, thereby reducing the hidden algebraic structure of integrability to a Hamiltonian-level conservation law. Since the Reshetikhin condition is equivalent to conservation of the total energy current, this Hamiltonian-level criterion is also experimentally accessible. This result establishes a quantum counterpart of the Liouville--Arnold theorem for isotropic spin chains, stating that Yang--Baxter solvability is equivalent to an infinite hierarchy of local conserved quantities. Our result also simplifies substantially the search for integrable spin chains by replacing the search for R-matrices with a direct criterion on local Hamiltonians.
Comments11 pages, 4 figures, 1 table; Supplemental Material included (23 pages). Code available at https://github.com/sanatanim/reshetikhin and archived at https://doi.org/10.5281/zenodo.21721878
