Clustering of steady-state correlations in open systems with long-range interactions

TL;DR

This paper extends Lieb-Robinson bounds to open quantum systems with long-range interactions, demonstrating how correlations cluster in steady states and advancing understanding of dissipative quantum dynamics.

Contribution

It proves new Lieb-Robinson bounds for dissipative systems with long-range interactions and shows how these bounds imply correlation clustering in steady states.

Findings

Lieb-Robinson bounds are extended to open systems with power-law decaying interactions.

Correlation clustering is demonstrated in the steady states of such open systems.

Provides a foundation for analyzing entanglement in experimental dissipative quantum platforms.

Abstract

Lieb-Robinson bounds are powerful analytical tools for constraining the dynamic and static properties of non-relativistic quantum systems. Recently, a complete picture for closed systems that evolve unitarily in time has been achieved. In experimental systems, however, interactions with the environment cannot generally be ignored, and the extension of Lieb-Robinson bounds to dissipative systems which evolve non-unitarily in time remains an open challenge. In this work, we prove two Lieb-Robinson bounds that constrain the dynamics of open quantum systems with long-range interactions that decay as a power-law in the distance between particles. Using a combination of these Lieb-Robinson bounds and mixing bounds which arise from "reversibility" -- naturally satisfied for thermal environments -- we prove the clustering of correlations in the steady states of open quantum systems with long-range interactions. Our work provides an initial step towards constraining the steady-state entanglement structure for a broad class of experimental platforms, and we highlight several open directions regarding the application of Lieb-Robinson bounds to dissipative systems.