Leveraging recurrence in neural network wavefunctions for large-scale simulations of Heisenberg antiferromagnets on the square lattice

TL;DR

This paper introduces a transfer learning approach using recurrent neural network wavefunctions to efficiently simulate large-scale quantum antiferromagnetic systems, achieving accurate thermodynamic limit estimates.

Contribution

The study demonstrates the use of RNNs with transfer learning to simulate large 2D quantum systems, reducing computational costs and improving accuracy in ground state property estimation.

Findings

Achieved accurate ground state energies for systems with over 1,000 spins.

Systematically improved results with increased training time.

Obtained thermodynamic limit estimates consistent with literature.

Abstract

Machine-learning-based variational Monte Carlo simulations are a promising approach for targeting quantum many-body ground states, especially in two dimensions and in cases where the ground state is known to have a non-trivial sign structure. While many state-of-the-art variational energies have been reached with these methods for finite-size systems, little work has been done to use these results to extract information about the target state in the thermodynamic limit. In this work, we employ recurrent neural networks (RNNs) as a variational ans\"{a}tze, and leverage their recurrent nature to simulate the ground states of progressively larger systems through iterative retraining. This transfer learning technique allows us to simulate spin-$\frac{1}{2}$ systems on lattices with more than 1,000 spins without beginning optimization from scratch for each system size, thus reducing the demands for computational resources. In this study, we focus on the square-lattice antiferromagnetic Heisenberg model, where it is possible to carefully benchmark our results. We show that we are able to systematically improve the accuracy of the results from our simulations by increasing the training time, and obtain results for finite-sized lattices that are in good agreement with the literature values. Furthermore, we use these results to extract accurate estimates of the ground-state properties in the thermodynamic limit. This work demonstrates that RNN wavefunctions are able to extract accurate information about quantum many-body systems in the thermodynamic limit.