Machine Learning Accelerated Coarsening Dynamics of Charge Density Waves on a Square Lattice

Abstract

Within the Born–Oppenheimer approximation, charge density waves (CDWs) can be regarded as slow collective degrees of freedom, evolving under Model-A dynamics as classified in the Hohenberg–Halperin framework. The order parameter is updated using the Allen–Cahn equation, where domain wall velocity is governed by local curvature. Studying CDW coarsening on a square lattice is computationally challenging, as exact diagonalization scales as O(N³) and suffers from strong finite-size effects. To overcome this, we employ machine learning to predict effective forces directly, bypassing repeated diagonalizations and reducing the scaling to O(N). This enables simulations on substantially larger lattices, allowing us to investigate the coarsening behavior of randomly distorted CDW order parameters over time. Our results provide new insights into large-scale CDW dynamics and demonstrate how machine learning can unlock the study of emergent collective phenomena beyond conventional computational limits.