Matrix product ansatz for non-equilibrium quantum steady states

Abstract

We present a general construction of matrix product states for stationary density matrices of one-dimensional quantum spin systems kept out of equilibrium through boundary Lindblad dynamics. As an application we review the isotropic Heisenberg quantum spin chain which is closely related to the generator of the simple symmetric exclusion process. Exact and heuristic results as well as numerical evidence suggest a local quantum equilibrium and long-range correlations reminiscent of similar large-scale properties in classical stochastic interacting particle systems that can be understood in terms of fluctuating hydrodynamics.

arXiv commentPaper presented at conference Particle Systems and Partial Differential equations IV, Braga, 28-30 Nov 2016

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Cited by in corpus (3)

• Fluctuating hydrodynamics, current fluctuations and hyperuniformity in boundary-driven open quantum chains
• Solution of the Lindblad equation for spin helix states
• Strongly correlated non-equilibrium steady states with currents --- quantum and classical picture