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

Fuente: arXiv
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Main Authors: Moss, M. Schuyler, Wiersema, Roeland, Hibat-Allah, Mohamed, Carrasquilla, Juan, Melko, Roger G.
Format: Preprint
Published: 2025
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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
id 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