Graph neural network force fields for adiabatic dynamics of lattice Hamiltonians
This work provides an efficient method for large-scale dynamical simulations of correlated lattice systems, which is incremental as it builds on existing GNN approaches but applies them to a specific domain with symmetry constraints.
The authors tackled the problem of scalable and symmetry-consistent force-field models for quantum-accurate simulations by developing a graph neural network (GNN) framework for adiabatic dynamics of lattice Hamiltonians, achieving high force accuracy, linear scaling with system size, and enabling large-scale Langevin simulations that revealed dynamical scaling and slow coarsening in charge-density-wave ordering.
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.