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State-of-the-art approaches to extract transport coefficients of many-bodyquantum systems broadly fall into two categories: (i) they target thelinear-response regime in terms of equilibrium correlation functions of theclosed system; or (ii) they consider an open-system situation typically modeledby a Lindblad equation, where a nonequilibrium steady state emerges fromdriving the system at its boundaries. While quantitative agreement between (i)and (ii) has been found for selected model and parameter choices, alsodisagreement has been pointed out in the literature. Studying magnetizationtransport 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 intime, can remarkably be constructed just on the basis of correlation functionsin the closed system. We numerically illustrate this direct correspondence ofclosed-system and open-system dynamics, and show that it allows the treatmentof comparatively large open systems, usually only accessible to matrix productstate simulations. We also point out potential pitfalls when extractingtransport coefficients from nonequilibrium steady states in finite systems.

Spin-1/2 XXZ chain coupled to two Lindblad baths: Constructing nonequilibrium steady states from equilibrium correlation functions