Direct free energy calculation from ab initio path integral Monte Carlo simulations of warm dense matter

We carry out highly accurate \emph{ab initio} path integral Monte Carlo (PIMC) simulations to directly estimate the free energy of various warm dense matter systems including the uniform electron gas and hydrogen without any nodal restrictions or other approximations. Since our approach is based on an effective ensemble in a bosonic configuration space, it does not increase the computational complexity beyond the usual fermion sign problem. Its application to inhomogeneous cases such as an electronic system in a fixed external ion potential is straightforward and opens up the enticing possibility to benchmark density functional theory and other existing methods. Finally, it is not limited to warm dense matter, and can be applied to a gamut of other systems such ultracold atoms and electrons in quantum dots.