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For a long time,there have been huge discrepancies between different models and experiments conceing the liquid-liquid phase transition (LLPT) in dense hydrogen.We present the results of extensive calculations of the LLPT in dense hydrogen using the most expensive first-principle path-integral molecular dynamics simulations available.The nonlocal density functional rVV10 and the hybrid functional PBE0 are used to improve the description of the electronic structure of hydrogen.Of all the density functional theory calculations available,we report the most consistent results through quantum Monte Carlo simulations and coupled electron-ion Monte Carlo simulations of the LLPT in dense hydrogen.The critical point of the first-order LLPT is estimated to be above 2000 K according to the equation of state.Moreover,the metallization pressure obtained from the jump of dc electrical conductivity almost coincides with the plateau of equation of state.