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

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.

10 pages, 9 figures

References in corpus (9)

• Matrix Product Density Operators: Simulation of finite-T and dissipative systems
• Restricted-Boltzmann-Machine Learning for Solving Strongly Correlated Quantum Systems
• Neural-Network Approach to Dissipative Quantum Many-Body Dynamics
• Weak binding between two aromatic rings: feeling the van der Waals attraction by quantum Monte Carlo methods
• Variational Quantum Monte Carlo Method with a Neural-Network Ansatz for Open Quantum Systems
• Variational neural network ansatz for steady states in open quantum systems
• Variational principle for steady states of dissipative quantum many-body systems
• Constructing neural stationary states for open quantum many-body systems
• Charge and spin transport in strongly correlated one-dimensional quantum systems driven far from equilibrium