Locality Estimates for Quantum Spin Systems

TL;DR

This paper reviews recent advances in understanding the locality properties of quantum spin systems, including sharper bounds on their dynamics, proofs of exponential clustering, and implications for multi-dimensional theorems.

Contribution

It provides a refined Lieb-Robinson bound and demonstrates its applications to quasi-locality, clustering, and multi-dimensional quantum spin system theorems.

Findings

Sharper Lieb-Robinson bounds for quantum spin systems.

Proof of the Exponential Clustering Theorem.

Discussion of multi-dimensional Lieb-Schultz-Mattis Theorem.

Abstract

We review some recent results that express or rely on the locality properties of the dynamics of quantum spin systems. In particular, we present a slightly sharper version of the recently obtained Lieb-Robinson bound on the group velocity for such systems on a large class of metric graphs. Using this bound we provide expressions of the quasi-locality of the dynamics in various forms, present a proof of the Exponential Clustering Theorem, and discuss a multi-dimensional Lieb-Schultz-Mattis Theorem.