The liquid-liquid phase transition of dense hydrogen using machine-learned interatomic potentials trained on quantum-monte carlo data

We investigate the liquid–liquid phase transition (LLPT) in dense hydrogen using two message-passing graph neural network potentials (MACE and DPA3) trained on quantum Monte Carlo (QMC) data. Our models are trained on an expanded version of the publicly available QMC hydrogen database (https://qmc-hamm.hub.yt/index.html), which now includes over 5,000 configurations near the LLPT. Molecular dynamics simulations employing these machine-learned potentials reveal a first-order liquid–liquid transition, identified through finite-size scaling analysis from 300 to 10,000 protons. Both MACE and DPA3 reproduce the phase transition under slightly different thermodynamic conditions, reflecting model-dependent sensitivity to the underlying potential energy surface. We further estimate the critical points for both hydrogen and deuterium, providing new insights into the behavior of hydrogen under extreme conditions.