论文标题
通过分离变量的相关函数：XXX自旋链
Correlation functions by Separation of Variables: the XXX spin chain
论文作者
论文摘要
我们解释了如何在简单模型的情况下在变量分离的量子版本的框架内计算零温度的相关函数：XXX Heisenberg Spin 1/2的XXX Heisenberg链，具有扭曲（Quasi-Periodic）边界条件。在抗周期边界条件的情况下，我们首先详细介绍了我们方法的所有步骤。该模型可以通过引入不均匀性参数在SOV框架中解决。然后，本地运算符对本征态的作用自然而然地以这些不均匀参数的多种总和来表达。我们解释了如何将这些总和上的不均匀性参数转换为多个轮廓积分。通过集成轮廓之外的极点的残基来评估这些多个积分，我们将此动作重写为涉及百特多项式根部的总和，以及无穷大的极点的贡献。我们表明，无穷大的杆的贡献在热力学极限中消失，并且我们在此极限中恢复了零温度相关性功能功能功能功能功能功能功能均以Bethe Ansatz或通过Q-vertex Operator对Infinite体积模型的研究来获得的多个积分表示。我们最终表明，该方法可以很容易地被推广到更一般的非对格扭曲的情况下：随后修改了相关函数的不同术语的相应权重，但是我们在热力学限制中恢复了相同的多个积分表示，而不是在周期性或抗生物的情况下与周期性或抗periodic的情况相同，从而证明了对相关功能的独立性的独立性。
We explain how to compute correlation functions at zero temperature within the framework of the quantum version of the Separation of Variables (SoV) in the case of a simple model: the XXX Heisenberg chain of spin 1/2 with twisted (quasi-periodic) boundary conditions. We first detail all steps of our method in the case of anti-periodic boundary conditions. The model can be solved in the SoV framework by introducing inhomogeneity parameters. The action of local operators on the eigenstates are then naturally expressed in terms of multiple sums over these inhomogeneity parameters. We explain how to transform these sums over inhomogeneity parameters into multiple contour integrals. Evaluating these multiple integrals by the residues of the poles outside the integration contours, we rewrite this action as a sum involving the roots of the Baxter polynomial plus a contribution of the poles at infinity. We show that the contribution of the poles at infinity vanishes in the thermodynamic limit, and that we recover in this limit for the zero-temperature correlation functions the multiple integral representation that had been previously obtained through the study of the periodic case by Bethe Ansatz or through the study of the infinite volume model by the q-vertex operator approach. We finally show that the method can easily be generalized to the case of a more general non-diagonal twist: the corresponding weights of the different terms for the correlation functions in finite volume are then modified, but we recover in the thermodynamic limit the same multiple integral representation than in the periodic or anti-periodic case, hence proving the independence of the thermodynamic limit of the correlation functions with respect to the particular form of the boundary twist.
