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

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.

arXiv comment18 pages, 2 figures. Comments welcome

References in corpus (24)

• Quantum information with Rydberg atoms
• Decoherence Free Subspaces for Quantum Computation
• Pseudo-Hermiticity versus PT Symmetry: The necessary condition for the reality of the spectrum of a non-Hermitian Hamiltonian
• The Quantum Jump Approach to Dissipative Dynamics in Quantum Optics
• An Area Law for One Dimensional Quantum Systems
• Engineered 2D Ising interactions on a trapped-ion quantum simulator with hundreds of spins
• Realizing a lattice spin model with polar molecules
• Programmable Quantum Simulations of Spin Systems with Trapped Ions
• Lieb-Robinson bounds and the generation of correlations and topological quantum order
• Towards the fast scrambling conjecture
• Exponentially slow heating in periodically driven many-body systems
• Scalable Architecture for a Room Temperature Solid-State Quantum Information Processor
• Nearly-linear light cones in long-range interacting quantum systems
• The Dynamics of 1D Quantum Spin Systems Can Be Approximated Efficiently
• Lieb-Robinson Bound and Locality for General Markovian Quantum Dynamics
• Quantum logarithmic Sobolev inequalities and rapid mixing
• Finite speed of quantum scrambling with long range interactions
• Persistence of locality in systems with power-law interactions
• Full-Counting Many-Particle Dynamics: Nonlocal and Chiral Propagation of Correlations
• Entanglement area laws for long-range interacting systems
• Fast State Transfer and Entanglement Renormalization Using Long-Range Interactions
• Absence of fast scrambling in thermodynamically stable long-range interacting systems
• Dynamical phase transitions in sampling complexity
• Optimal Frobenius light cone in spin chains with power-law interactions