论文标题
通过融合，嵌入形态和反弹流动的任何紧凑表示中有理gl（n）自旋链变量的分离
Separation of variables for rational gl(n) spin chains in any compact representation, via fusion, embedding morphism and Backlund flow
论文作者
论文摘要
我们提出了一种方法，以在每个站点和具有通用扭曲的周期性边界条件下，在有限的有限维不可减少的表示中，在合理的集成$ \ mathfrak {gl}（n）$ spin链中分离变量。首先，我们构建了一个基础，该基础是对角较高版本的Sklyanin B-operator的基础。该结构是基于将$ \ mathfrak {gl}（k）$ spin链嵌入$ \ mathfrak {gl} {gl}（k+1）$ spin链中的递归用法。然后，我们表明，可以通过反向插头转换的融合转移矩阵的作用来构建相同的基础，从而将Bethe波函数分配到Baxter Q函数中上升的Slater决定因素的产物中。最后，我们构建了升高和降低操作员 - 共轭动量 - 作为在B的零零 - 分离变量的百特Q-操作器中的正常订购的wronskian表达式。拟议的建筑的直接结果是，伯特（Bethe）代数包括最大可能的相互通勤费用数量，这是伯特方程式完成的必要特性。
We propose a way to separate variables in a rational integrable $\mathfrak{gl}(n)$ spin chain with an arbitrary finite-dimensional irreducible representation at each site and with generic twisted periodic boundary conditions. Firstly, we construct a basis that diagonalises a higher-rank version of the Sklyanin B-operator; the construction is based on recursive usage of an embedding of a $\mathfrak{gl}(k)$ spin chain into a $\mathfrak{gl}(k+1)$ spin chain which is induced from a Yangian homomorphism and controlled by dual diagonals of Gelfand-Tsetlin patterns. Then, we show that the same basis can be equivalently constructed by action of Backlund-transformed fused transfer matricies, whence the Bethe wave functions factorise into a product of ascending Slater determinants in Baxter Q-functions. Finally, we construct raising and lowering operators -- the conjugate momenta -- as normal-ordered Wronskian expressions in Baxter Q-operators evaluated at zeros of B -- the separated variables. It is an immediate consequence of the proposed construction that the Bethe algebra comprises the maximal possible number of mutually commuting charges -- a necessary property for Bethe equations to be complete.
