Phase transitions of correlated systems from graph neural networks with quantum embedding techniques

Correlated systems represent a class of materials that are difficult to describe through traditional electronic structure methods. The computational cost of simulating the structural dynamics of such systems, with correlation effects considered, is substantial. Here, we investigate the structural dynamics of $f$- and $d$-electron correlated systems by integrating quantum embedding techniques with interatomic potentials derived from graph neural networks. For cerium, a prototypical correlated $f$-electron system, we use density functional theory with the Gutzwiller approximation to generate training data due to efficiency with which correlation effects are included for large multiorbital systems. For nickel oxide, a prototypical correlated $d$-electron system, advancements in computational capabilities now permit the use of full dynamical mean field theory to obtain energies and forces. We train neural networks on these data to create a model of the potential energy surface, enabling rapid and effective exploration of structural dynamics. Utilizing these potentials, we delineate transition pathways between the $\ensuremath{\alpha}$, ${\ensuremath{\alpha}}^{\ensuremath{'}}$, and ${\ensuremath{\alpha}}^{\ensuremath{''}}$ phases of cerium and predict the melting curve of nickel oxide. Our results demonstrate the potential of machine learning potentials to accelerate the study of strongly correlated systems, offering a scalable approach to explore and understand the complex physics governing these materials.