  We compute the electrical conductivity for liquid hydrogen at high pressure
using quantum Monte Carlo. The method uses Coupled Electron-Ion Monte Carlo to
generate configurations of liquid hydrogen. For each configuration correlated
sampling of electrons is performed in order to calculate a set of lowest
many-body eigenstates and current-current correlation functions of the system,
which are summed over in the many-body Kubo formula to give AC electrical
conductivity directly. The extrapolated DC conductivity at 3000 K for several
densities shows a liquid semiconductor to liquid-metal transition at high
pressure. Our results are in good agreement with shock-wave data.
