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For a long time, there have been huge discrepancies between different modelsand experiments concerning the liquid-liquid phase transition (LLPT) in densehydrogen. In this work, we present the results of extensive calculations of theLLPT in dense hydrogen using the most expensive first-principle path-integralmolecular dynamics simulations available. The nonlocal density functional rVV10and hybrid functional PBE0 are used to improve the description of theelectronic structure of hydrogen. Of all the density functional theorycalculations available, we report the most consistent results through quantumMonte Carlo simulations and coupled electron-ion Monte Carlo simulations of theLLPT in dense hydrogen. The critical point of the first-order LLPT is estimatedabove 2000 K according to the equation of state. Moreover, the metallizationpressure obtained from the jump of dc electrical conductivity almost coincideswith the plateau of equation of state.

Towards the same line of liquid-liquid phase transition of dense hydrogen from various theoretical predictions