Many-body Effects in the Warm Dense Electron Gas Revealed by Variational Diagrammatic Monte Carlo method

The study of warm dense matter (WDM), which exists in various astrophysical objects and state-of-the-art experiments with high-power lasers, is of high current interest for many applications. However, due to the lack of a thorough theoretical description of WDM, accurate numerical data for the density response in finite-temperature electron gas is essential. In this work, we investigate the local field correction (LFC), which incorporates all the quantum many-body effects in the density response of the warm dense electron gas by the state-of-the-art variational diagrammatic Monte Carlo technique. We establish the static LFC G(q,T) for a wide range of the momentum q and the temperature T with high accuracy. Our numerical results for G(q,T) demonstrate nontrivial quantum-to-classical crossover in the warm dense regime, and reveal a novel scaling relation G(q/√T) at the high-T and large-q limits. We further prove and numerically verify the asymptotic expression of G(q) at the large-q limit, allowing a systematic calculation of the exchange-correlation kernel K_xc(r,T) in real space for various temperatures. Our study paves the way for more systematic ab initio calculations of WDM, and is directly relevant for experiments probing the many-body effects.