Graph neural network force fields for adiabatic dynamics of lattice Hamiltonians

TL;DR

This paper introduces a graph neural network framework for simulating the adiabatic dynamics of lattice Hamiltonians, achieving high accuracy, scalability, and transferability, demonstrated on the Holstein model and large-scale Langevin simulations.

Contribution

It presents a GNN-based force-field model that enforces lattice symmetries directly, enabling efficient, accurate, and scalable simulations of large correlated lattice systems.

Findings

High force accuracy on the Holstein model

Linear scaling with system size

Successful large-scale Langevin simulations revealing dynamical phenomena

Abstract

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.