Liquid-liquid phase transition of hydrogen and its critical point: Analysis from <i>ab initio</i> simulation and a machine-learned potential

We simulate high-pressure hydrogen in its liquid phase close to molecular dissociation using a machine-learned interatomic potential. The model is trained with density functional theory forces and energies, with the Perdew-Burke-Ernzerhof (PBE) exchange-correlation functional. We show that an accurate NequIP model, an E(3)-equivariant neural network potential, accurately reproduces the phase transition present in PBE. Moreover, the computational efficiency of this model allows for substantially longer molecular-dynamics trajectories, enabling us to perform a finite-size scaling analysis to distinguish between a crossover and a true first-order phase transition. We locate the critical point of this transition, the liquid-liquid phase transition, at 1200-1300 K and 155-160 GPa, a temperature lower than most previous estimates and close to the melting transition.