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

• URL: http://arxiv.org/abs/2110.15368v1
• Date: Thu, 28 Oct 2021 18:00:00 GMT
• Title: Clustering of steady-state correlations in open systems with long-range interactions
• Authors: Andrew Y. Guo, Simon Lieu, Minh C. Tran, Alexey V. Gorshkov
• Abstract summary: We prove two Lieb-Robinson bounds that constrain the dynamics of open quantum systems with long-range interactions that decay as a power-law. Our work provides an initial step towards constraining the steady-state entanglement structure for a broad class of experimental platforms.
• Score: 0.6554326244334866
• License: http://creativecommons.org/licenses/by/4.0/
• 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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