Coarsening dynamics of charge density waves in Holstein-Hubbard model: Machine learning enabled large-scale dynamical simulations

We develop a machine learning (ML) force-field model to enable large-scale adiabatic dynamical simulations of the Holstein-Hubbard model on a square lattice. At small Hubbard repulsion, the system exhibits a robust charge density wave (CDW) order at half-filling. 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, however, is computationally very expensive for large systems. 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. Our large-scale thermal quench simulations uncover an anomalous growth of the CDW domains that deviates significantly from the expected Allen-Cahn law for phase ordering of Ising-type order parameter field. Moreover, we observe an intriguing non-monotonic dependence of CDW coarsening on the Hubbard repulsion, indicating nontrivial interplay between electron correlation and CDW dynamics.