TY - JOUR

T1 - Real-time broadening of bath-induced density profiles from closed-system correlation functions

AU - Heitmann, Tjark

AU - Richter, Jonas

AU - Herbrych, Jacek

AU - Gemmer, Jochen

AU - Steinigeweg, Robin

N1 - Funding Information: This work has been funded by the Deutsche Forschungsgemeinschaft (DFG), under Grants No. 397107022 (GE 1657/3-2) and No. 397067869 (STE 2243/3-2), within the DFG Research Unit FOR 2692, under Grant No. 355031190. We acknowledge computing time at the HPC3 at University Osnabrück, which has been funded by the DFG under Grant No. 456666331. J.R. acknowledges funding from the European Union's Horizon Europe research and innovation programme under the Marie Skłodowska-Curie Grant Agreement No. 101060162, and the Packard Foundation through a Packard Fellowship in Science and Engineering.

PY - 2023/8/3

Y1 - 2023/8/3

N2 - 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.

AB - 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.

UR - http://www.scopus.com/inward/record.url?scp=85167968280&partnerID=8YFLogxK

U2 - 10.48550/arXiv.2210.10528

DO - 10.48550/arXiv.2210.10528

M3 - Article

AN - SCOPUS:85167968280

VL - 108

JO - Physical Review E

JF - Physical Review E

SN - 2470-0045

IS - 2

M1 - 024102

ER -