Machine learning for phase ordering dynamics of charge density waves

Abstract

We present a machine learning (ML) framework for large-scale dynamical simulations of charge density wave (CDW) states. The charge modulation in a CDW state is often accompanied by a concomitant structural distortion, and the adiabatic evolution of a CDW order is governed by the dynamics of the lattice distortion. Calculation of the electronic contribution to the driving forces for large systems, however, is computationally very expensive. Assuming the principle of locality for electron systems, a neural-network model is developed to accurately and efficiently predict local electronic forces with input from neighborhood configurations. Importantly, the ML model enables a linear complexity algorithm for dynamical simulations of CDWs. As a demonstration, we apply our approach to investigate the phase ordering dynamics of the Holstein model, a canonical system of CDW order. Our large-scale simulations reveal an intriguing growth of CDW domains that deviates significantly from the expected Allen-Cahn law for phase ordering of Ising-type order parameter field. This anomalous domain growth could be attributed to the complex structure of domain walls in this system. Our paper highlights the promising potential of ML-based force-field models for dynamical simulations of functional electronic materials.