



01670nas a2200145   4500008004100000245008900041210006900130260001500199520119300214100002001407700001601427700001901443700002501462856003701487       2021                        eng d00aClustering of steady-state correlations in open systems with long-range interactions0 aClustering of steadystate correlations in open systems with long  c10/28/20213 a<p>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 &quot;reversibility&quot; -- 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.</p>1 aGuo, Andrew, Y.1 aLieu, Simon1 aTran, Minh, C.1 aGorshkov, Alexey, V.  uhttps://arxiv.org/abs/2110.15368