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.

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.

The Lindblad master equation is one of the main approaches to open quantum systems. While it has been
widely applied in the context of condensed matter systems to study properties of steady states in the limit
of long times, the actual route to such steady states has attracted less attention yet. Here, we investigate the
nonequilibrium dynamics of spin chains with a local coupling to a single Lindblad bath and analyze the transport
properties of the induced magnetization. Combining typicality and equilibration arguments with stochastic
unraveling, we unveil for the case of weak driving that the dynamics in the open system can be constructed
on the basis of correlation functions in the closed system, which establishes a connection between the Lindblad
approach and linear response theory at finite times. In this way, we provide a particular example where closed and
open approaches to quantum transport agree strictly. We demonstrate this fact numerically for the spin-1/2 XXZ
chain at the isotropic point and in the easy-axis regime, where superdiffusive and diffusive scaling is observed,
respectively.

The Lindblad master equation is one of the main approaches to open quantum systems. While it has been
widely applied in the context of condensed matter systems to study properties of steady states in the limit
of long times, the actual route to such steady states has attracted less attention yet. Here, we investigate the
nonequilibrium dynamics of spin chains with a local coupling to a single Lindblad bath and analyze the transport
properties of the induced magnetization. Combining typicality and equilibration arguments with stochastic
unraveling, we unveil for the case of weak driving that the dynamics in the open system can be constructed
on the basis of correlation functions in the closed system, which establishes a connection between the Lindblad
approach and linear response theory at finite times. In this way, we provide a particular example where closed and
open approaches to quantum transport agree strictly. We demonstrate this fact numerically for the spin-1/2 XXZ
chain at the isotropic point and in the easy-axis regime, where superdiffusive and diffusive scaling is observed,
respectively.