Lieb-Robinson Bounds and the Exponential Clustering Theorem

TL;DR

This paper establishes a Lieb-Robinson bound for discrete quantum systems, demonstrating that a spectral gap leads to exponential clustering in the ground state, thus connecting dynamical bounds with ground state properties.

Contribution

The paper introduces a Lieb-Robinson bound applicable to a broad class of quantum systems, linking spectral gaps to exponential decay of correlations.

Findings

Lieb-Robinson bound derived for quantum systems

Spectral gap implies exponential clustering

Ground state correlations decay exponentially

Abstract

We give a Lieb-Robinson bound for the group velocity of a large class of discrete quantum systems which can be used to prove that a non-vanishing spectral gap implies exponential clustering in the ground state of such systems.