Propagation of Correlations in Quantum Lattice Systems

TL;DR

This paper proves a simple version of the Lieb-Robinson bound for quantum lattice systems with polynomial decay interactions, establishing limits on how quickly correlations can develop over time.

Contribution

It offers a straightforward proof of the Lieb-Robinson bound and extends it to systems with polynomial decay interactions, clarifying correlation propagation limits.

Findings

Established an upper bound on correlation growth rate.

Proved the existence of dynamics for polynomial decay interactions.

Provided a simplified proof of the Lieb-Robinson bound.

Abstract

We provide a simple proof of the Lieb-Robinson bound and use it to prove the existence of the dynamics for interactions with polynomial decay. We then use our results to demonstrate that there is an upper bound on the rate at which correlations between observables with separated support can accumulate as a consequence of the dynamics.