标题： 静态和动态自旋关联在有限温度下的Kitaev模型通过格林函数运动方程 显示英文标题

标题： Static and Dynamical Spin Correlations in the Kitaev Model at Finite Temperatures via Green's Function Equation of Motion

摘要： 克塔夫模型因其精确可解性以及可能容纳非阿贝尔任意子而广受关注，仍然是量子自旋液体和拓扑相研究的焦点。尽管现有文献大多采用马约拉纳费米子技术来分析该模型，尤其是在零温度下，但其有限温度行为通过其他方法进行的探索仍不够深入。在本文中，我们使用自旋格林函数形式来研究克塔夫模型的有限温度特性。这种方法能够计算诸如自旋关联、磁化率和动态自旋结构因子等关键物理量，为系统热动力学提供了重要的见解。在求解自旋格林函数的运动方程时，我们通过一种解耦近似截断多自旋格林函数的层次结构，该近似在高温下表现出特别的准确性。我们的结果与基于马约拉纳的数值模拟有若干相似之处，但也出现了显著的差异。具体而言，静态和动态自旋-自旋关联函数不仅捕捉到了$\mathbb{Z}_2$通量激发，还捕捉到了简单的自旋翻转激发，后者掩盖了前者。有趣的是，即使没有明确假设分数化，我们在低温下的自旋磁化率和自旋弛豫率的结果仍然表明存在费米子自由度。这项研究提供了一种补充方法来理解克塔夫模型的热性质，这可能对未来的实验和理论研究具有相关性。 显示英文摘要

摘要： The Kitaev model, renowned for its exact solvability and potential to host non-Abelian anyons, remains a focal point in the study of quantum spin liquids and topological phases. While much of the existing literature has employed Majorana fermion techniques to analyze the model, particularly at zero temperature, its finite-temperature behavior has been less thoroughly explored via alternative approaches. In this paper, we investigate the finite-temperature properties of the Kitaev model using the spin Green's function formalism. This approach enables the computation of key physical quantities such as spin correlations, magnetic susceptibility, and the dynamical spin structure factor, offering crucial insights into the system's thermal dynamics. In solving the equation of motion for the spin Green's function, we truncate the hierarchy of multi-spin Green's functions using a decoupling approximation, which proves to be particularly accurate at high temperatures. Our results show several similarities with Majorana-based numerical simulations, though notable differences emerge. Specifically, both static and dynamical spin-spin correlation functions capture not only $\mathbb{Z}_2$ flux excitations but also simple spin-flip excitations, with the latter overshadowing the former. Interestingly, without explicitly assuming fractionalization, our results for the spin susceptibility and spin relaxation rate still suggest the presence of fermionic degrees of freedom at low temperatures. This study provides a complementary approach to understanding the thermal properties of the Kitaev model, which could be relevant for future experiments and theoretical investigations.