  Using Quantum Monte Carlo (QMC) calculations, we investigate the
insulator-metal transition observed in liquid hydrogen at high pressure. Below
the critical temperature of the transition from the molecular to the atomic
liquid, the fundamental electronic gap closure occurs abruptly, with a small
discontinuity reflecting the weak first-order transition in the thermodynamic
equation of state. Above the critical temperature, molecular dissociation sets
in while the gap is still open. When the gap closes, the decay of the
off-diagonal reduced density matrix shows that the liquid enters a gapless, but
localized phase: there is a cross-over between the insulating and the metallic
liquids. Compared to different DFT functionals, our QMC calculations provide
larger values for the fundamental gap and the electronic density of states
close to the band edges, indicating that optical properties from DFT
potentially benefit from error cancellations.
