Thermodynamics of the uniform electron gas: Fermionic path integral Monte Carlo simulations in the restricted grand canonical ensemble

The uniform electron gas (UEG) is one of the key models for the understanding of warm dense matter—an exotic, highly compressed state of matter between solid and plasma phases. The difficulty in modelling the UEG arises from the need to simultaneously account for Coulomb correlations, quantum effects, and exchange effects, as well as finite temperature. The most accurate results so far were obtained from quantum Monte Carlo (QMC) simulations with a variety of representations. However, QMC for electrons is hampered by the fermion sign problem. Here, we present results from a novel fermionic propagator path integral Monte Carlo in the restricted grand canonical ensemble. The ab initio simulation results for the spin-resolved pair distribution functions and static structure factor are reported for two isotherms (T in the units of the Fermi temperature). Furthermore, we combine the results from the linear response theory in the Singwi-Tosi-Land-Sjölander scheme with the QMC data to remove finite-size errors in the interaction energy. We present a new corrected parametrization for the interaction energy and the exchange–correlation free energy in the thermodynamic limit, and benchmark our results against the restricted path integral Monte Carlo by Brown et al. [Phys. Rev. Lett. 110 , 146405 (2013)] and configuration path integral Monte Carlo/permutation-blocking path integral Monte Carlo by Dornheim et al. [Phys. Rev. Lett. 117 , 115701 (2016)].