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Open-system tensor networks and Kramers' crossover for quantum transport



Gabriela Wojtowicz, Justin E. Elenewski, Marek Rams, Michael P. Zwolak


Tensor networks are a powerful tool for many-body ground-states with limited entanglement. These methods can nonetheless fail for certain time-dependent processes - such as quantum trans- port or quenches - where entanglement growth is linear in time. Matrix product state decompositions of the resulting out-of-equilibrium states require a bond dimension that grows exponentially, imposing a hard limit on simulation timescales. However, if the reservoir modes of a closed system are arranged according to their scattering structure, the entanglement growth can be made logarithmic. Here, we extend this ansatz to open systems via extended reservoirs that have explicit relaxation. This enables transport calculations that can access true steady-states, time-dynamics, and periodic driving. We demonstrate the approach by calculating the transport characteristics of an open, interacting system. These results open a path to rigorous, many-body transport calculations.
Physical Review A (Atomic, Molecular and Optical Physics)


Wojtowicz, G. , Elenewski, J. , Rams, M. and Zwolak, M. (2020), Open-system tensor networks and Kramers' crossover for quantum transport, Physical Review A (Atomic, Molecular and Optical Physics), [online],, (Accessed July 24, 2024)


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Created May 11, 2020, Updated October 12, 2021