AbstractThe melting temperature of solid hydrogen drops with pressure above ~65 GPa, suggesting that a liquid state might exist at low temperatures. It has also been suggested that this low-temperature liquid state might be non-molecular and metallic, although evidence for such behaviour is lacking. Here we report results for hydrogen at high pressures using ab initio methods, which include a description of the quantum motion of the protons. We determine the melting temperature as a function of pressure and find an atomic solid phase from 500 to 800 GPa, which melts at <200 K. Beyond this and up to 1,200 GPa, a metallic atomic liquid is stable at temperatures as low as 50 K. The quantum motion of the protons is critical to the low melting temperature reported, as simulations with classical nuclei lead to considerably higher melting temperatures of ~300 K across the entire pressure range considered.