  We present a new Monte Carlo method which couples Path Integral for finite
temperature protons with Quantum Monte Carlo for ground state electrons, and we
apply it to metallic hydrogen for pressures beyond molecular dissociation. We
report data for the equation of state for temperatures across the melting of
the proton crystal. Our data exhibit more structure and higher melting
temperatures of the proton crystal than Car-Parrinello Molecular Dynamics
results. This method fills the gap between high temperature electron-proton
Path Integral and ground state Diffusion Monte Carlo methods.
