The uniform electron gas at warm dense matter conditions

A second major aspect of this review is the use of our ab initio simulation results to test previous theories, including restricted PIMC, finite-temperature Green functions, the classical mapping by Perrot and Dharma-wardana, and various dielectric methods such as the random phase approximation, or the Singwi-Tosi-Land-Sjölander (both in the static and quantum versions), Vashishta-Singwi and the recent Tanaka scheme for the local field correction. Thus, for the first time, thorough benchmarks of the accuracy of important approximation schemes regarding various quantities such as different energies, in particular the exchange-correlation free energy, and the static structure factor, are possible. In the final part of this paper, we outline a way how to rigorously extend our QMC studies to the inhomogeneous electron gas. We present first ab initio data for the static density response and for the static local field correction.