Melting line of dense hydrogen from hierarchical machine learning using diffusion Monte Carlo data*

The phase transitions of dense hydrogen are of interest in astrophysics and in condensed matter physics. Ab initio simulations suffer from errors due to small system sizes, while empirical potentials lack the accuracy needed to describe these transitions. To minimize these errors, we use diffusion Monte Carlo (DMC) forces to train a hierarchical machine-learning potential and perform large-scale two-phase classical molecular dynamics and quantum path integral molecular dynamics simulations to estimate the melting line for dense hydrogen in the pressure range 50-200 GPa. We estimate the effect on the melting temperature coming from the assumed density functional, from the machine-learning procedures, and from the nuclear zero-point motion.