标题： 利用神经网络波函数中的递归进行海森堡反铁磁体的大规模模拟：三角晶格 显示英文标题

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

摘要： 变分蒙特卡洛模拟对于理解量子多体系统至关重要，尤其是在哈密顿量存在阻挫且基态波函数具有非平凡符号结构的情况下。 本文中，我们使用循环神经网络（RNN）波函数参数来研究三角晶格反铁磁海森堡模型（TLAHM），晶格大小可达$30\times30$。 在最近的一项研究中 [M. S. Moss 等人, arXiv:2502.17144]，作者展示了如何通过迭代重新训练RNN波函数，以合理数量的计算资源获得多个晶格尺寸的变分结果。 该研究着眼于无符号问题的方形晶格反铁磁海森堡模型，展示了有利的缩放特性，允许准确地将有限尺寸外推到热力学极限。 相比之下，我们的当前结果详细说明了模拟具有符号问题的TLAHM的相对难度。 我们发现，通过明智选择基变换可以显著提高模拟的准确性。 我们还表明，通过使用变分神经退火（一种最小化伪自由能的替代优化技术），也可以获得类似的好处。 最终，我们能够得到与文献中值非常接近的TLAHM在热力学极限下的基态性质估计，这表明RNN波函数为研究受阻量子多体系统的有限尺寸缩放提供了强大的工具箱。 显示英文摘要

摘要： 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.