Machine learning for quantum spin dynamics in and out of equilibrium*

We propose a new numerical framework based on machine learning (ML) potentials to enable large-scale adiabatic quantum Landau-Lifshitz-Gilbert (LLG) dynamics simulations of itinerant electron magnets. Such metallic spin systems are central to novel phenomena such as colossal magnetoresistance and spin-transfer torques. Our approach is similar in spirit to the Behler-Parrinello ML scheme that has become a cornerstone of large-scale molecular dynamics method with the accuracy of quantum calculation. Based on the principle of locality for electronic systems, the total electronic energy is partitioned into contributions from individual spins which depend only on the local environment. A neural network model is then trained from exact solutions on small systems to approximate the complex dependence of the local energy on the neighborhood spin configuration. We further develop a novel descriptor to ensure the spin rotation symmetry as well as the discrete lattice symmetry. Our work opens new avenues for using deep-learning models to simulate and understand large-scale dynamical phenomena in functional magnetic systems.