Open System Tensor Networks and Kramers’ Crossover for Quantum Transport

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 transport or quenches. 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, in the case of transport, if the reservoir modes of a closed system are arranged according to their scattering structure, the entanglement growth can be mitigated. Here, we apply this ansatz to open systems via extended reservoirs that have explicit relaxation. This enables transport calculations that can access steady states, time dynamics and noise, and periodic driving (e.g., Floquet states). We demonstrate the approach by calculating the transport characteristics of an open, interacting system.
[1] GW, JEE Elenewski, MM Rams, and M Zwolak, Phys. Rev. A 101, 050301 (R)