一维各向异性XYZ自旋链模型的热力学极限研究

本项目将采用一种巧妙的热力学分析方法来研究U(1)对称性破缺的XYZ自旋链模型的热力学极限。我们的中心思想是使用零根将转移矩阵本征值函数参数化为多项式函数。借助于非均匀转移矩阵的算符恒等式以及给定的非均匀参数密度，求解得到零根的分布密度函数。最后，通过解析延拓得到对计算物理量至关重要的均匀转移矩阵的零根密度。应用该方法，我们将求解一般边界条件和反周期边界条件下XYZ模型的热力学极限，并通过综合研究模型边界参数对零根分布的影响从而得到与边界参数有关的奇异元激发和边界能等物理量。通过该研究，我们将获得一个普适的求解U(1)对称性破缺可积模型的热力学极限的方法。

In this project, the thermodynamic limit of the XYZ spin chain model without U(1) symmetry will be studied by a novel analytic method. Our central idea lies in that the spectrum of transfer matrix will be directly parameterized into a polynomial function by using zeros roots. With the help of the operator identity of the inhomogeneous transfer matrix and the given distribution density of the site-dependent inhomogeneity, the distribution density function of the zero roots can be obtained. Then, the density of the zero roots of the homogeneous transfer matrix, which is crucial to compute the physical quantities, can be obtained via analytic continuation. Using this method, we will solve the thermodynamic limit of XYZ model with general non-diagonal boundary conditions and anti-periodic boundary conditions, and obtain the physical quantities such as element excitation and surface energy related to the boundary parameters by comprehensively studying the distribution of the zero roots affected by the boundary parameters. Through this study, we will obtain a universal method to solve the thermodynamic limit of the integrable models without U(1) symmetry.