Lieb-Robinson Bounds and Quasi-locality for the Dynamics of Many-Body Quantum Systems

TL;DR

This paper reviews a recently established Lieb-Robinson bound that describes how information propagates in many-body quantum systems, highlighting the connection between commutator estimates and quasi-locality.

Contribution

It presents a comprehensive review of the proof of Lieb-Robinson bounds and their implications for the quasi-local behavior of quantum dynamics.

Findings

Lieb-Robinson bounds establish finite speed of information propagation.

Connection between commutator estimates and quasi-locality is elucidated.

Examples illustrate the applicability of the bounds to various quantum systems.

Abstract

We review a recently proven Lieb-Robinson bound for general, many-body quantum systems with bounded interactions. Several basic examples are discussed as well as the connection between commutator estimates and quasi-locality.