Lieb-Robinson Bound at Finite Temperature

TL;DR

This paper extends the Lieb-Robinson bound to finite-temperature quantum systems, providing bounds on information propagation speed and correlation clustering for various interaction ranges.

Contribution

It introduces a novel method to extend the Lieb-Robinson bound to finite temperatures and different interaction types using combinatoric graph techniques.

Findings

Bound applies to short-range, exponential, and long-range interactions.

Provides a new way to count clusters in cluster expansions.

Discusses limitations and potential applications of the finite-temperature bound.

Abstract

The Lieb-Robinson bound shows that the speed of propagating information in a nonrelativistic quantum lattice system is bounded by a finite velocity, which entails the clustering of correlations. In this paper, we extend the Lieb-Robinson bound to quantum systems at finite temperature by calculating the dynamical correlation function at nonzero temperature for systems whose interactions are respectively short-range, exponentially-decaying and long-range. We introduce a simple way of counting the clusters in a cluster expansion by using the combinatoric generating functions of graphs. Limitations and possible applications of the obtained bound are also discussed.