Accurate exchange-correlation energies for the warm dense electron gas

The accurate treatment of matter at high temperatures and densities is of increasing importance to many fields in physics and chemistry, with applications ranging from planetary physics to inertial confinement fusion and plasmonic catalysis. Faithfully including the effects of temperature in density functional theory simulations of warm dense matter requires accurate results for the uniform electron gas (UEG) across the whole temperature-density plane. While accurate ground state quantum Monte Carlo data have existed for over 30 years \footnote{Phys. Rev. Lett. 45, 566 (1980)}, there remains significant disagreement between results obtained using different path integral Monte Carlo methods at finite temperature \footnote{Phys. Rev. Lett. 110, 146405 (2013)}\footnote{Phys. Rev. Lett. 115, 130402 (2015)}. To resolve this disagreement, we use the systematically improvable density matrix quantum Monte Carlo method \footnote{Phys. Rev. B 89, 245124 (2014)}\footnote{J. Chem. Phys. 143, 044116 (2015)} to calculate the exchange-correlation energy of the UEG. We also demonstrate how the evaluation of free energies emerges naturally from our method.