Lindblad dynamics from spatio-temporal correlation functions in nonintegrable spin-1/2 chains with different boundary conditions

We investigate the Lindblad equation in the context of boundary-driven magnetization transport in spin-$1/2$ chains. Our central question is whether the nonequilibrium steady state of the open system, including its buildup in time, can be described on the basis of the dynamics in the closed system. To this end, we rely on a previous work [Phys. Rev. B 108, L201119 (2023)], where a description in terms of spatio-temporal correlation functions has been suggested in the case of weak driving and small system-bath coupling. Because this work has focused on integrable systems and periodic boundary conditions, we here extend the analysis in three directions: We (i) consider nonintegrable systems, (ii) take into account open boundary conditions and other bath-coupling geometries, and (iii) provide a comparison to time-evolving block decimation. While we find that nonintegrability plays a minor role, the choice of the specific boundary conditions can be crucial, due to potentially nondecaying edge modes. Our large-scale numerical simulations suggest that a description based on closed-system correlation functions is an useful alternative to already existing state-of-the-art approaches.