Revisiting boundary-driven method for transport: Finite-size effects and the role of system-bath coupling

Understanding transport in interacting quantum many-body systems is a central challenge in condensed matter and statistical physics. Numerical studies typically rely on two main approaches: Dynamics of linear-response functions in closed systems and Markovian dynamics governed by master equations for boundary-driven open systems. While the equivalence of their dynamical behavior has been explored in recent studies, a systematic comparison of the transport coefficients obtained from these two classes of methods remains an open question. Here, we address this gap by comparing and contrasting the dc diffusion constant Ddc computed from the aforementioned two approaches. We find a clear mismatch between the two, with Ddc exhibiting a strong dependence on the system-bath coupling for the boundary-driven technique, highlighting fundamental limitations of such a method in calculating the transport coefficients related to asymptotic dynamical behavior of the system. We trace the origin of this mismatch to the incorrect order of limits of time t → ∞ and system size L→ ∞, which we argue to be intrinsic to boundary-driven setups. As a practical resolution, we advocate computing only time-dependent transport coefficients within the boundary-driven framework, which show excellent agreement with those obtained from the Kubo formalism based on closed-system dynamics, up to a timescale set by the system size. This leads us to interpret the sensitivity of the dc diffusion constant on the system-bath coupling strength in an open system as a potential diagnostic for finite-size effects.