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

TL;DR

This paper demonstrates how recurrent neural network wavefunctions can effectively simulate large-scale frustrated quantum systems, specifically the triangular-lattice antiferromagnetic Heisenberg model, by improving accuracy through basis transformations and neural annealing.

Contribution

It introduces the use of RNN wavefunctions for the TLAHM, showing improved accuracy with basis rotations and variational neural annealing, advancing scalable simulations of frustrated quantum systems.

Findings

Achieved ground-state estimates in the thermodynamic limit close to literature values.

Improved simulation accuracy via basis rotation and neural annealing techniques.

Demonstrated the effectiveness of RNN wavefunctions for large-scale frustrated systems.

Abstract

Variational Monte Carlo simulations have been crucial for understanding quantum many-body systems, especially when the Hamiltonian is frustrated and the ground-state wavefunction has a non-trivial sign structure. In this paper, we use recurrent neural network (RNN) wavefunction ans\"{a}tze to study the triangular-lattice antiferromagnetic Heisenberg model (TLAHM) for lattice sizes up to $30\times30$. In a recent study [M. S. Moss et al. arXiv:2502.17144], the authors demonstrated how RNN wavefunctions can be iteratively retrained in order to obtain variational results for multiple lattice sizes with a reasonable amount of compute. That study, which looked at the sign-free, square-lattice antiferromagnetic Heisenberg model, showed favorable scaling properties, allowing accurate finite-size extrapolations to the thermodynamic limit. In contrast, our present results illustrate in detail the relative difficulty in simulating the sign-problematic TLAHM. We find that the accuracy of our simulations can be significantly improved by transforming the Hamiltonian with a judicious choice of basis rotation. We also show that a similar benefit can be achieved by using variational neural annealing, an alternative optimization technique that minimizes a pseudo free energy. Ultimately, we are able to obtain estimates of the ground-state properties of the TLAHM in the thermodynamic limit that are in close agreement with values in the literature, showing that RNN wavefunctions provide a powerful toolbox for performing finite-size scaling studies for frustrated quantum many-body systems.