State-of-the-art approaches to extract transport coefficients of many-body quantum systems broadly fall into two categories: (i) they target the linear-response regime in terms of equilibrium correlation functions of the closed system; or (ii) they consider an open-system situation typically modeled by a Lindblad equation, where a nonequilibrium steady state emerges from driving the system at its boundaries. While quantitative agreement between (i) and (ii) has been found for selected model and parameter choices, also disagreement has been pointed out in the literature. Studying magnetization transport in the spin-1/2 XXZ chain, we here demonstrate that at weak driving, the nonequilibrium steady state in an open system, including its buildup in time, can remarkably be constructed just on the basis of correlation functions in the closed system. We numerically illustrate this direct correspondence of closed-system and open-system dynamics, and show that it allows the treatment of comparatively large open systems, usually only accessible to matrix product state simulations. We also point out potential pitfalls when extracting transport coefficients from nonequilibrium steady states in finite systems.

Our research has been funded by the DeutscheForschungsgemeinschaft (DFG), Projects No. 397107022(GE 1657/3-2), No. 397300368 (MI 1772/4-2), and No.397067869 (STE 2243/3-2), within DFG Research UnitFOR 2692, Grant no. 355031190. J.R. acknowledges funding from the European Union's Horizon Europe research andinnovation programme, Marie Skłodowska-Curie Grant No.101060162, and the Packard Foundation through a PackardFellowship in Science and Engineering. We gratefully acknowledge the Gauss Centre for Supercomputing e.V. forfunding this project by providing computing time on the GCSSupercomputer JUWELS at Jülich Supercomputing Centre (JSC). Z.L. and S.N. acknowledge support by Projects No.J1-2463 and No. P1-0044 program of the Slovenian ResearchAgency, EU via QuantERA grant T-NiSQ, and also computing time for the TEBD calculations at the supercomputer Vegaat the Institute of Information Science (IZUM) in Maribor,Slovenia. We also acknowledge computing time at the HPC3at University Osnabrück, which has been funded by the DFG,Grant No. 456666331.