Quantum Transport in Open Spin Chains using Neural-Network Quantum States

TL;DR

This paper introduces a neural network approach using restricted Boltzmann machines to accurately model non-equilibrium steady states in asymmetric open quantum spin chains, overcoming previous computational challenges.

Contribution

It presents a novel optimization and sampling method that improves the fidelity of neural-network quantum states for asymmetric dissipative systems, exploiting symmetries in the Lindblad operator.

Findings

High-fidelity steady state approximations achieved

Results agree with known spin current behaviors

Sampling technique effectively handles asymmetry

Abstract

In this work we study the treatment of asymmetric open quantum systems with neural networks based on the restricted Boltzmann machine. In particular, we are interested in the non-equilibrium steady state current in the boundary-driven (anisotropic) Heisenberg spin chain. We address previously published difficulties in treating asymmetric dissipative systems with neural-network quantum states and Monte-Carlo sampling and present an optimization method and a sampling technique that can be used to obtain high-fidelity steady state approximations of such systems. We point out some inherent symmetries of the Lindblad operator under consideration and exploit them during sampling. We show that local observables are not always a good indicator of the quality of the approximation and finally present results for the spin current that are in agreement with known results of simple open Heisenberg chains.