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

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.

10 pages, 4 figues

References in corpus (6)

• Multi-party entanglement in graph states
• Lieb-Robinson bounds and the generation of correlations and topological quantum order
• Propagation of Correlations in Quantum Lattice Systems
• Nearly-linear light cones in long-range interacting quantum systems
• Lieb-Robinson Bounds for Harmonic and Anharmonic Lattice Systems
• Geometric phase of an atom in a magnetic storage ring

Cited by in corpus (7)

• Locality and digital quantum simulation of power-law interactions
• Realizing distance-selective interactions in a Rydberg-dressed atom array
• Tightening the Lieb-Robinson Bound in Locally-Interacting Systems
• Lieb-Robinson bounds for open quantum systems with long-ranged interactions
• Many-Body Physics in Small Systems: Observing the Onset and Saturation of Correlation in Linear Atomic Chains
• Inferred-variance uncertainty relations in the presence of quantum entanglement
• Locality, Correlations, Information, and non-Hermitian Quantum Systems