Kubo’s canonical correlation functions (canonical correlators) describe the static response of a system in equilibrium to infinitesimal local perturbations. Knowing their decay properties with respect to spatial distance is important for many theoretical and experimental applications. For a thermal state of a system with short-range interactions, we prove that any knowledge of the decay rate of ordinary correlators readily translates into that of canonical correlators. As the former have been extensively studied, our result can lead to many new results on the latter. Throughout the paper, we use the framework of infinite-volume quantum lattice model. However, the method we use is adaptable for other physical scenarios not considered in this paper.

Kubo 的典型相关函数（典型相关器）描述了处于平衡状态的系统对无穷小的局部扰动的静态响应。了解它们相对于空间距离的衰减特性对于许多理论和实验应用很重要。对于具有短程相互作用的系统的热状态，我们证明了对普通相关器衰减率的任何了解都可以很容易地转化为规范相关器的衰减率。由于前者已被广泛研究，我们的结果可以导致关于后者的许多新结果。在整篇论文中，我们使用了无限体积量子点阵模型的框架。但是，我们使用的方法适用于本文未考虑的其他物理场景。