Leveraging recurrence in neural network wavefunctions for large-scale simulations of Heisenberg antiferromagnets on the triangular lattice
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| Main Authors: | , , , , |
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| Format: | Preprint |
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2025
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| _version_ | 1866918159546580992 |
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| author | Moss, M. Schuyler Wiersema, Roeland Hibat-Allah, Mohamed Carrasquilla, Juan Melko, Roger G. |
| author_facet | Moss, M. Schuyler Wiersema, Roeland Hibat-Allah, Mohamed Carrasquilla, Juan Melko, Roger G. |
| contents | 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 ansätze 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. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2505_20406 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Leveraging recurrence in neural network wavefunctions for large-scale simulations of Heisenberg antiferromagnets on the triangular lattice Moss, M. Schuyler Wiersema, Roeland Hibat-Allah, Mohamed Carrasquilla, Juan Melko, Roger G. Strongly Correlated Electrons Disordered Systems and Neural Networks Quantum Physics 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 ansätze 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. |
| title | Leveraging recurrence in neural network wavefunctions for large-scale simulations of Heisenberg antiferromagnets on the triangular lattice |
| topic | Strongly Correlated Electrons Disordered Systems and Neural Networks Quantum Physics |
| url | https://arxiv.org/abs/2505.20406 |