Decay of multi-point correlation functions in $\mathbb{Z}^d$

TL;DR

This paper establishes bounds on multi-point correlation functions in lattice systems, providing new insights into decay properties and localization phenomena in disordered quantum systems.

Contribution

It proves multi-point correlation bounds in $ olinebreak bZ^d$ for arbitrary dimensions, answering open questions and applying results to Ising models and disordered systems.

Findings

Multi-point correlation bounds for $bZ^d$ proven.

First examples of multi-point dynamical localization in disordered systems.

Answers to open questions by Sims-Warzel and Aza-Bru-Siqueira Pedra.

Abstract

We prove multi-point correlation bounds in $\mathbb{Z}^d$ for arbitrary $d\geq 1$ with symmetrized distances, answering open questions proposed by Sims-Warzel \cite{SW} and Aza-Bru-Siqueira Pedra \cite{ABP}. As applications, we prove multi-point correlation bounds for the Ising model on $\mathbb{Z}^d$, and multi-point dynamical localization in expectation for uniformly localized disordered systems, which provides the first examples of this conjectured phenomenon by Bravyi-K\"onig \cite{BK}.