# Lieb-Robinson bounds on $n$-partite connected correlation functions

## TL;DR

This paper extends Lieb-Robinson bounds to multipartite connected correlation functions, revealing that such correlations can rapidly reach large values, contrasting with bipartite cases, and providing explicit examples.

## Contribution

It generalizes Lieb-Robinson bounds to multipartite correlations and demonstrates their potential for rapid growth, including exponential scaling with system size.

## Key findings

- Multipartite connected correlators can reach unit value in constant time.
- They can also grow exponentially with system size in constant time.
- Explicit examples of systems exhibiting these behaviors are provided.

## Abstract

Lieb and Robinson provided bounds on how fast bipartite connected correlations can arise in systems with only short-range interactions. We generalize Lieb-Robinson bounds on bipartite connected correlators to multipartite connected correlators. The bounds imply that an $n$-partite connected correlator can reach unit value in constant time. Remarkably, the bounds also allow for an $n$-partite connected correlator to reach a value that is exponentially large with system size in constant time, a feature which stands in contrast to bipartite connected correlations. We provide explicit examples of such systems.