标题： 量子自旋链中来自单个守恒定律的可积性 显示英文标题

标题： Integrability from a Single Conservation Law in Quantum Spin Chains

摘要： 我们证明对于具有有限范围相互作用的量子自旋链，一个称为Reshetikhin条件的特定守恒定律的存在意味着存在无限多个局部守恒量，即可积性。 这表明与Yang--Baxter方程解相关的整个守恒定律层次已经编码在最低非平凡的守恒定律中。 结合最近关于不可积性的严格结果，我们的定理大大限制了仅包含有限但大量局部守恒量的部分可积系统的可能性。 我们的工作为系统地识别新的可积模型建立了严格的理论基础，并加深了对量子自旋链中守恒定律结构的代数理解。 显示英文摘要

摘要： We prove that for quantum spin chains with finite-range interactions, the existence of a specific conservation law known as the Reshetikhin condition implies the presence of infinitely many local conserved quantities, i.e., integrability. This shows that the entire hierarchy of conservation laws associated with solutions of the Yang--Baxter equation is already encoded in the lowest nontrivial conservation law. Combined with recent rigorous results on nonintegrability, our theorem strongly restricts the possibility of partially integrable systems that admit only a finite but large number of local conserved quantities. Our work establishes a rigorous foundation for the systematic identification of new integrable models and deepens the algebraic understanding of conservation-law structures in quantum spin chains.