论文标题
量子自旋链的形式因子的渐近分析
Asymptotic analysis of the form-factors of quantum spin chains
论文作者
论文摘要
自长时间以来，量子整合系统一直是现代数学方法在物理系统研究中获得有趣结果的领域。相关函数的数值和渐近学的确切计算是量子整合模型理论中最重要的主题之一。在这种情况下，基于形式因素的计算方法已被证明是一种更有效的方法。在本文中，我们开发了一种基于代数贝尔·安萨兹（Bethe ansatz）的新方法，用于计算热力学极限中形式因子。它既适用于以及各向同性XXX海森伯格链的上下文，这是Fermi-Zone是非紧凑的临界模型的有趣案例的示例之一。在特定的两翼型形式因子的情况下，我们获得了封闭形式的确切结果，该结果与基于$ q $ vertex运算符代数的方法获得的先前结果匹配。然后将此方法推广到高旋子扇区中的形式因子，在该扇区中，我们找到了形式因子的降低的确定性表示，其中揭示了形式因子的高级结构。
Since a long-time, the quantum integrable systems have remained an area where modern mathematical methods have given an access to interesting results in the study of physical systems. The exact computations, both numerical and asymptotic, of the correlation function is one of the most important subject of the theory of the quantum integrable models. In this context an approach based on the calculation of form factors has been proved to be a more effective one. In this thesis, we develop a new method based on the algebraic Bethe ansatz for the computation of the form-factors in thermodynamic limit. It is both applied to and described in the context of isotropic XXX Heisenberg chain, which is one of the examples of an interesting case of critical models where the Fermi-zone is non-compact. In a particular case of two-spinon form-factors, we obtain an exact result in a closed-form which matches the previous result obtained from an approach based on $q$-vertex operator algebra. This method is then generalised to form-factors in higher spinon sectors where we find a reduced determinant representation for the form-factors, in which a higher-level structure for the form-factors is revealed.
