论文标题
循环编织组和可集成的模型
Loop braid groups and integrable models
论文作者
论文摘要
循环辫子组表征了扩展对象的交换，即循环在三维空间中，概括了编织组的概念，这些概念描述了在二维空间中描述点粒子的交换。它们对物理学的兴趣源于以下事实：它们以三个维度捕获了任何统计数据，而这些统计量否则仅在平面上仅存在于点粒子。在这里，我们探索了另一个方向，循环编织组的代数关系可以发挥作用 - 量子整合模型。我们表明，{\ it对称环编织组}自然可以引起杨 - 巴克斯特方程的解决方案，从而通过RTT关系证明了某些模型的整合性。对于对称循环辫子组的某些表示形式，我们获得了$ xxx $ - ，$ xxz $ - 和$ xyz $ -spin链的可集成变形。
Loop braid groups characterize the exchange of extended objects, namely loops, in three dimensional space generalizing the notion of braid groups that describe the exchange of point particles in two dimensional space. Their interest in physics stems from the fact that they capture anyonic statistics in three dimensions which is otherwise known to only exist for point particles on the plane. Here we explore another direction where the algebraic relations of the loop braid groups can play a role -- quantum integrable models. We show that the {\it symmetric loop braid group} can naturally give rise to solutions of the Yang--Baxter equation, proving the integrability of certain models through the RTT relation. For certain representations of the symmetric loop braid group we obtain integrable deformations of the $XXX$-, $XXZ$- and $XYZ$-spin chains.
