Machine-learned interatomic potentials of dense hydrogen from diffusion Monte Carlo

Many aspects of the phase diagram of dense hydrogen remain poorly understood, sometimes even qualitatively. Dense hydrogen is predicted become a high-temperature superconductor at sufficiently high pressure and is crucial in determining the structure of gas giant planets. Addressing the entire phase diagram with accurate ab initio simulations like diffusion Monte Carlo (DMC) is not currently feasible due to the computational cost, which limits studies to small system sizes. Recently, machine-learned interatomic potentials trained on ab initio data have been applied in large-scale molecular dynamics simulations to approach the accuracy of the ab initio methods without the finite size errors. Typically, these have relied on density functional theory to generate the training data. Here we present the first large-scale publicly accessible DMC database for dense hydrogen, which allows training of machine-learned potentials with DMC accuracy. Using this database, we determine the melting curve of molecular hydrogen as a function of pressure in the range 50-200 GPa. While at lower pressure our result agrees with previous theory and experiment, we find a substantially higher melting temperature at higher pressures.