General spin systems without genuinely multipartite nonlocality

TL;DR

This paper demonstrates that certain quantum spin systems with exponential decay of correlations do not exhibit genuine multipartite nonlocality, providing a new way to identify non-entangled states in many-body quantum systems.

Contribution

It introduces a method to determine the absence of genuine multipartite nonlocality in spin systems using Lieb-Robinson bounds and clustering theorems, which is a novel approach.

Findings

Ground and thermal states show no genuine multipartite nonlocality when regions are far apart.

Exponential decay of correlations implies only biseparable quantum correlations.

Results apply to systems with product initial states and short-range interactions.

Abstract

There are multipartite entangled states in many-body systems which may be potential resources in various quantum applications. There are lots of methods to witness specific entangled systems. However, no efficient method is available to explore many-body systems without multipartite entanglement. It may provide necessary restrictions for experimental preparations of multipartite entanglement. Our goal is to solve this problem for spin systems. The maximal effective velocity with propagation of information is bounded in quantum spin systems with short-range interactions from Lieb-Robinson's inequalities. This implies two clustering theorems for ground states and thermal states. With these propagation relations, we show that both the gapped ground state and thermal state at an upper-bounded inverse temperature have no genuine multipartite nonlocality when disjoint regions are far away from each other. The present $n$-particle system shows only biseparable quantum correlations when the propagation relations show exponential decay. Similar result holds for spin systems with product states as initial states. These results show interesting features of quantum many-body systems with exponential decay of correlations.