The uniform electron gas at high temperatures: ab initio path integral Monte Carlo simulations and analytical theory

We present extensive new Ab initio path integral Monte Carlo (PIMC) simulations of the uniform electron gas (UEG) in the high-temperature regime, $8\le \theta =k_{B}T/E_F\le 128$. This allows us to study the convergence of different properties towards the classical limit. In particular, we investigate the classical relation between the static structure factor $S\left(q\right)$ and the static local field correction $G\left(q\right)$, which is only fulfilled at low densities. Moreover, we compare our new results for the interaction energy to the parametrization of the UEG by Groth et al. (2017), which interpolates between PIMC results for $\theta \le 8$ and the Debye–Hückel limit, and to higher order analytical virial expansions. Finally, we consider the momentum distribution function $n\left(q\right)$ and find an interaction-induced increase in the occupation of the zero-momentum state even for $\theta \gtrsim 32$. All PIMC data are freely available online, and can be used as input for improved parametrizations and as a rigorous benchmark for approximate methods.