论文标题
形式因子和通过分离变量的较高旋转链的变量的完整基础
Form-factors and complete basis of observables via separation of variables for higher rank spin chains
论文作者
论文摘要
我们在本文中考虑的可集成的SL（N）旋转链不仅是量子整合系统的原型示例，而且是具有广泛应用的系统。对于这些模型，我们将变量（FSOV）技术的功能分离与一个称为字符投影的新工具一起计算一组完整的运算符的所有矩阵元素，我们将其称为主要操作员，基于对角线，将保守费用的塔式作为Q-Tunctions中的保守指控塔。然后，基于这些结果，我们为任意分解状态之间的多个主要操作员组合的形式形式得出了类似的决定因素形式，这些状态尤其包括，尤其是贝斯伯特矢量和伯特载体，并具有任意曲折的伯特载体。我们证明，一组主要操作员会生成完整的自旋链扬吉安人。此外，我们在SOV基础上得出了这些操作员的表示，允许一个人与任意数量的主要运营商计算相关函数。最后，我们表明多个插入的可用组合包括Sklyanin的Sov B运算符。结果，我们能够使用最小的成分（即FSOV方法和SOV基础的结构）来得出SL（N）自旋链的B算子。
Integrable sl(N) spin chains, which we consider in this paper, are not only the prototypical example of quantum integrable systems but also systems with a wide range of applications. For these models we use the Functional Separation of Variables (FSoV) technique with a new tool called Character Projection to compute all matrix elements of a complete set of operators, which we call principal operators, in the basis diagonalising the tower of conserved charges as determinants in Q-functions. Building up on these results we then derive similar determinant forms for the form-factors of combinations of multiple principal operators between arbitrary factorizable states, which include, in particular, off-shell Bethe vectors and Bethe vectors with arbitrary twists. We prove that the set of principal operators generates the complete spin chain Yangian. Furthermore, we derive the representation of these operators in the SoV bases allowing one to compute correlation functions with an arbitrary number of principal operators. Finally, we show that the available combinations of multiple insertions includes Sklyanin`s SoV B operator. As a result, we are able to derive the B operator for sl(N) spin chains using a minimal set of ingredients, namely the FSoV method and the structure of the SoV basis.
