Detailing emergent quantum phenomena predicted for hydrogen at high densities remains a key challenge in condensed matter physics. A first-order issue is stabilization of the quantum fluid relative to solid phases at multimegabar $(>100\mathrm{GPa})$ pressures, a problem for which accurate large-scale simulations can play a critical role in predicting behavior beyond the range of current pressure-temperature $\left(P\text{−}T\right)$ experiments. Here, we developed a machine-learned interatomic potential for hydrogen trained on accurate diffusion quantum Monte Carlo data, including total energies and atomic forces, which allows us to investigate the melting curve of hydrogen over a broad range of pressures. Our simulations predict a broad melting maximum near 1000 K at $100–150\mathrm{GPa}$, followed by a leveling off in the melting temperature at higher pressure, in good agreement with experiment. Beyond the range of current experiments, the simulations predict that hydrogen melts near room temperature and is remarkably independent of pressure from 500 to 900 GPa. Our results suggest that hydrogen does not have a fluid ground state up to terapascal pressure and provide a baseline for understanding this exotic quantum material at ultrahigh pressures.

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• High-pressure studies
• Liquid-solid phase transition
• Quantum fluids & solids
• Solid hydrogen
• Diffusion quantum Monte Carlo
• Machine learning
• Path integrals