Kinetics of Peierls dimerization transition: Machine learning force-field approach

TL;DR

This paper develops a machine learning force-field to simulate charge-density-wave dynamics driven by Peierls instability, enabling large-scale, accurate, and efficient non-equilibrium simulations of lattice-electron interactions.

Contribution

It introduces a generalized neural network force field for Peierls systems, achieving linear scaling and capturing complex domain coarsening behaviors in CDW dynamics.

Findings

Uncovered a two-stage CDW domain coarsening process.

Identified a power-law growth with exponent ~0.7 in early dynamics.

Observed crossover to classical Allen-Cahn scaling at late times.

Abstract

We present a machine learning (ML) force-field framework for simulating the non-equilibrium dynamics of charge-density-wave (CDW) order driven by the Peierls instability. Since the Peierls distortion arises from the coupling between lattice displacements and itinerant electrons, evaluating the adiabatic forces during time evolution is computationally intensive, particularly for large systems. To overcome this bottleneck, we develop a generalized Behler-Parrinello neural-network architecture -- originally formulated for ab initio molecular dynamics -- to accurately and efficiently predict forces from local structural environments. Using the locality of electronic responses, the resulting ML force field achieves linear scaling efficiency while maintaining quantitative accuracy. Large-scale dynamical simulations using this framework uncover a two-stage coarsening behavior of CDW domains: an early-time regime characterized by a power-law growth $L \sim t^{\alpha}$ with an effective exponent $\alpha \approx 0.7$, followed by a crossover to the Allen-Cahn scaling $L \sim \sqrt{t}$ at late times. The enhanced early-time coarsening is attributed to anisotropic domain-wall motion arising from electron-mediated directional interactions. This work demonstrates the promise of ML-based force fields for multiscale dynamical modeling of condensed-matter lattice models.