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arXiv · 2110.15368

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

Andrew Y. Guo·Simon Lieu·Minh C. Tran·Alexey V. Gorshkov
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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.

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Andrew Y. Guo, Simon Lieu, Minh C. Tran, Alexey V. Gorshkov. 2021-10-28. Clustering of steady-state correlations in open systems with long-range interactions. https://arxiv.org/abs/2110.15368

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