Spatial Decay of Kubo's Canonical Correlation Function

TL;DR

This paper proves that the decay rate of canonical correlation functions in quantum lattice models can be directly inferred from the decay properties of ordinary correlators, facilitating new insights into their behavior.

Contribution

It establishes a general method to derive decay properties of Kubo's canonical correlators from known decay rates of ordinary correlators in quantum lattice systems.

Findings

Decay rates of canonical correlators can be deduced from ordinary correlators.

The method applies to infinite-volume quantum lattice models.

Framework is adaptable to other physical scenarios.

Abstract

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.