Open System Tensor Networks and Kramers' Crossover for Quantum Transport

TL;DR

This paper introduces a tensor network approach for simulating quantum transport in open systems, overcoming entanglement growth limitations and enabling scalable calculations of steady states, dynamics, and noise.

Contribution

It presents a novel tensor network ansatz for open quantum systems with explicit relaxation, allowing efficient simulation of transport phenomena beyond previous limitations.

Findings

Successfully computed transport properties of an interacting open system.

Demonstrated access to steady states, time dynamics, and noise in quantum transport.

Showed that entanglement growth can be managed logarithmically in this framework.

Abstract

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 - 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, 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 made logarithmic. 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. These results open a path to scalable and numerically systematic many-body transport calculations with tensor networks.