Leveraging recurrence in neural network wavefunctions for large-scale simulations of Heisenberg antiferromagnets

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 ansätze, 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-1/2 systems on very large lattices without beginning optimization from scratch for each system size, thus reducing the demands for computational resources. We first examine the square-lattice Heisenberg antiferromagnet, where it is possible to carefully benchmark our results. We also study the more challenging, sign-problematic triangular-lattice Heisenberg antiferromagnet. In both cases, we show that we are able to systematically improve the accuracy of our simulations by increasing the training time. Furthermore, we use our finite-size results to extract accurate estimates of  ground-state properties in the thermodynamic limit. These works demonstrate that RNN wavefunctions are able to extract accurate information about quantum many-body systems in the thermodynamic limit.