Coarsening dynamics of charge density waves in Peierls model : Machine learning force-field approach

We present a machine-learning (ML) force-field framework for nonequilibrium simulations of charge-density-wave (CDW) order in a two-dimensional Peierls model with next-nearest-neighbor hopping. The ML model, trained on exact forces and built on locality of electronic responses, replaces repeated diagonalizations in an adiabatic scheme and reduces the force evaluation to linear complexity, enabling genuinely large-scale coarsening studies. Following a thermal quench, the CDW correlation length displays a clear two-stage growth: an accelerated regime with exponent $\alpha \!\approx\! 0.7$ that crosses over to the Allen–Cahn value $\alpha \!=\! 1/2$ at late times. The acceleration arises from an electron-mediated anisotropy in the Peierls susceptibility of phonons near $\mathbf{Q}=(\pi,\pi)$, which favors diagonal domain-wall alignment and modifies the coarsening pathway. Our paper highlights the ML speed-up and the anisotropy mechanism reveal scaling departures that become accessible with large-scale Peierls dynamics.