用图神经网络构建对称性保持的力场，实现大尺度晶格系统动力学模拟。
Graph neural network force fields for adiabatic dynamics of lattice Hamiltonians
- 通过消息传递和权重共享直接实现晶格平移与点群对称性约束。
- 训练后力场精度高，计算量线性增长，可直接推广至大规模体系。
- 适用于需要高精度与可扩展性的关联晶格系统动力学研究者。
可扩展且保持对称性的力场模型对于将量子精确模拟拓展到大时空尺度至关重要。尽管基于描述符的神经网络可通过精心设计特征来融入晶格对称性，我们发现图神经网络（GNN）提供了一种更简洁统一的替代方案，其通过局部消息传递和权重共享直接强制执行离散晶格平移与点群对称性。我们开发了基于GNN的晶格哈密顿量绝热动力学力场框架，并在半经典霍尔斯坦模型上进行了验证。该模型基于精确对角化数据训练，实现了高力场精度、严格线性缩放与直接向大规模晶格的可迁移性。得益于这一可扩展性，我们开展了热淬火后电荷密度波有序的大型朗之万模拟，揭示了动态标度规律及异常缓慢的亚-艾伦-考恩粗化行为。这些结果确立了GNN作为对称感知、大规模关联晶格系统动力学模拟的优雅高效架构。
原文摘要 · Abstract (English)
Scalable and symmetry-consistent force-field models are essential for extending quantum-accurate simulations to large spatiotemporal scales. While descriptor-based neural networks can incorporate lattice symmetries through carefully engineered features, we show that graph neural networks (GNNs) provide a conceptually simpler and more unified alternative in which discrete lattice translation and point-group symmetries are enforced directly through local message passing and weight sharing. We develop a GNN-based force-field framework for the adiabatic dynamics of lattice Hamiltonians and demonstrate it for the semiclassical Holstein model. Trained on exact-diagonalization data, the GNN achieves high force accuracy, strict linear scaling with system size, and direct transferability to large lattices. Enabled by this scalability, we perform large-scale Langevin simulations of charge-density-wave ordering following thermal quenches, revealing dynamical scaling and anomalously slow sub--Allen--Cahn coarsening. These results establish GNNs as an elegant and efficient architecture for symmetry-aware, large-scale dynamical simulations of correlated lattice systems.
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