Spatial decay of Kubo’s canonical correlation functions

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 spatial distance is important for many theoretical and experimental applications. For thermal state short-range interactions, we prove that any knowledge rate ordinary correlators readily translates into correlators. As former have been extensively studied, our result can lead new results on latter. Throughout paper, use framework infinite-volume quantum lattice model. However, method adaptable other physical scenarios not considered this paper.