Equivariant Neural Networks for Force-Field Models of Lattice Systems
This work addresses the need for more general and transferable force-field models in condensed-matter lattice simulations, offering a data-driven approach that avoids system-specific hand-crafted descriptors, though it is incremental as it adapts existing equivariant neural network concepts to lattice systems.
The authors tackled the problem of constructing general, transferable machine-learning force fields for lattice systems with coupled electronic and structural degrees of freedom, by introducing a symmetry-preserving framework based on equivariant neural networks that embeds discrete point-group and internal symmetries, and demonstrated its utility through large-scale dynamical simulations of the Holstein Hamiltonian that faithfully captured mesoscale evolution of the symmetry-breaking phase.
Machine-learning (ML) force fields enable large-scale simulations with near-first-principles accuracy at substantially reduced computational cost. Recent work has extended ML force-field approaches to adiabatic dynamical simulations of condensed-matter lattice models with coupled electronic and structural or magnetic degrees of freedom. However, most existing formulations rely on hand-crafted, symmetry-aware descriptors, whose construction is often system-specific and can hinder generality and transferability across different lattice Hamiltonians. Here we introduce a symmetry-preserving framework based on equivariant neural networks (ENNs) that provides a general, data-driven mapping from local configurations of dynamical variables to the associated on-site forces in a lattice Hamiltonian. In contrast to ENN architectures developed for molecular systems -- where continuous Euclidean symmetries dominate -- our approach aims to embed the discrete point-group and internal symmetries intrinsic to lattice models directly into the neural-network representation of the force field. As a proof of principle, we construct an ENN-based force-field model for the adiabatic dynamics of the Holstein Hamiltonian on a square lattice, a canonical system for electron-lattice physics. The resulting ML-enabled large-scale dynamical simulations faithfully capture mesoscale evolution of the symmetry-breaking phase, illustrating the utility of lattice-equivariant architectures for linking microscopic electronic processes to emergent dynamical behavior in condensed-matter lattice systems.