  We combine ab initio path integral Monte Carlo (PIMC) simulations with fixed
ion configurations from density functional theory molecular dynamics (DFT-MD)
simulations to solve the electronic problem for hydrogen under warm dense
matter conditions [M.B\"ohme et. al. Phys.Rev.Lett.(in print)]. The problem of
path collapse due to the Coulomb attraction is avoided by utilizing the pair
approximation, which is compared against the simpler Kelbg pair-potential. We
find very favourable convergence behaviour towards the former. Since we do not
impose any nodal restrictions, our PIMC simulations are afflicted with the
notorious fermion sign problem, which we analyse in detail. While
computationally demanding, our results constitute an exact benchmark for other
methods and approximations such as DFT. Our set-up gives us the unique
capability to study important properties of warm dense hydrogen such as the
electronic static density response and exchange--correlation (XC) kernel
without any model assumptions, which will be very valuable for a variety of
applications such as the interpretation of experiments and the development of
new XC functionals.
