Abstract:
Understanding transport in quantum many-body systems is a central challenge in condensed matter and statistical physics. Theoretical studies typically rely on two main approaches: Dynamics of linear-response functions in closed systems and Lindblad dynamics in open systems with boundary driving. While the equivalence of their dynamical behavior has been explored in recent studies [1,2], a systematic comparison of the transport coefficients obtained from these two classes of approaches is a less explored question. Here [3], we address this question by comparing and contrasting the diffusion constants from the two approaches. We find a clear mismatch and in particular a strong dependence on the system-bath coupling for the open spin-1/2 XXZ chain with boundary driving. We trace the origin of this mismatch to an incorrect order of limits of time t -> ∞ and system size L -> ∞, which we argue to be intrinsic to the open system. As a practical resolution, we advocate to study the whole time dependence of transport coefficients, which convincingly agree for the two approaches, up to a time scale set by the system size.
[1] T. Heitmann, J. Richter, F. Jin, S. Nandy, Z. Lenarčič, J. Herbrych, K. Michielsen, H. De Raedt, J. Gemmer, R. Steinigeweg, Physical Review B 108, L201119 (2023).
[2] M. Kraft, J. Richter, F. Jin, S. Nandy, J. Herbrych, K. Michielsen, H. De Raedt, J. Gemmer, R. Steinigeweg, Physical Review Research 6, 023251 (2024).
[3] M. Kempa, M. Kraft, S. Nandy, J. Herbrych, J. Wang, J. Gemmer, R. Steinigeweg, arXiv:2507.16528.