高阶自旋链的观测量分离变量的形状因子和完备基
Form-factors and complete basis of observables via separation of variables for higher rank spin chains
摘要：
本文所研究的可积sl（N）自旋链不仅是量子可积系统的典型例子，而且是具有广泛应用的系统。对于这些模型，我们使用变量的功能分离（FSoV）技术与一个新的工具，称为字符投影计算所有矩阵元素的一套完整的运营商，我们称之为主运营商，在基础上对角化塔的保守电荷在Q函数的决定因素。建立在这些结果，然后我们推导出类似的行列式形式的任意可因子化状态之间的多个主算子的组合的形状因子，其中包括，特别是，壳外Bethe矢量和任意扭曲的Bethe矢量。我们证明了主算子集生成完备的自旋链Yangian。此外，我们推导出这些运营商的表示在SoV基地允许一个计算关联函数与任意数量的主要运营商。最后，我们表明，多个插入的可用组合包括Sklyanin的SoV B运营商。因此，我们能够使用最小成分集，即FSoV方法和SoV基的结构，导出sl（N）自旋链的B算子。
英文摘要：
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.
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