We present a scalable machine learning (ML) force-field model for the adiabatic dynamics of cooperative Jahn-Teller (JT) systems. Large scale dynamical simulations of the JT model also shed light on the orbital ordering dynamics in colossal magnetoresistance manganites. The JT effect in these materials describes the distortion of local oxygen octahedra driven by a coupling to the orbital degrees of freedom of $e_g$ electrons. An effective electron-mediated interaction between the local JT modes leads to a structural transition and the emergence of long-range orbital order at low temperatures. Assuming the principle of locality, a deep-learning neural-network model is developed to accurately and efficiently predict the electron-induced forces that drive the dynamical evolution of JT phonons. A group-theoretical method is utilized to develop a descriptor that incorporates the combined orbital and lattice symmetry into the ML model. Large-scale Langevin dynamics simulations, enabled by the ML force-field models, are performed to investigate the coarsening dynamics of the composite JT distortion and orbital order after a thermal quench. The late-stage coarsening of orbital domains exhibits pronounced freezing behaviors which are likely related to the unusual morphology of the domain structures. Our work highlights a promising avenue for multi-scale dynamical modeling of correlated electron systems.

翻译：我们提出了一种用于合作Jahn-Teller（JT）系统绝热动力学的可扩展机器学习（ML）力场模型。JT模型的大规模动力学模拟也揭示了庞磁阻锰酸盐中轨道有序化的动力学。这些材料中的JT效应描述了由$e_g$电子轨道自由度耦合驱动的局部氧八面体畸变。局部JT模式之间有效的电子介导相互作用导致了结构相变以及在低温下出现长程轨道有序。基于局域性原理，我们开发了一种深度学习神经网络模型，以准确高效地预测驱动JT声子动力学演化的电子诱导力。我们利用群论方法开发了一种描述符，将轨道与晶格的组合对称性纳入ML模型。借助ML力场模型，我们进行了大规模朗之万动力学模拟，以研究热淬火后复合JT畸变与轨道有序的粗化动力学。轨道畴的后期粗化表现出显著的冻结行为，这可能与畴结构的不寻常形态有关。我们的工作为关联电子系统的多尺度动力学建模指明了一条有前景的途径。