Ab Initio Quantum Monte Carlo Simulations of the Uniform Electron Gas without Fixed Nodes

Abstract

The uniform electron gas (UEG) at finite temperature is of key relevance for many applications in the warm dense matter regime, e.g. dense plasmas and laser excited solids. Also, the quality of density functional theory calculations crucially relies on the availability of accurate data for the exchange-correlation energy. Recently, new benchmark results for the N = 33 spin-polarized electrons at high density, r_s = r/a_B <= 4 and low temperature, have been obtained with the configuration path integral Monte Carlo (CPIMC) method [T. Schoof et al., Phys. Rev. Lett. 115, 130402 (2015)]. To achieve these results, the original CPIMC algorithm [T. Schoof et al., Contrib. Plasma Phys. 51, 687 (2011)] had to be further optimized to cope with the fermion sign problem (FSP). It is the purpose of this paper to give detailed information on the manifestation of the FSP in CPIMC simulations of the UEG and to demonstrate how it can be turned into a controllable convergence problem. In addition, we present new thermodynamic results for higher temperatures. Finally, to overcome the limitations of CPIMC towards strong coupling, we invoke an independent method|the recently developed permutation blocking path integral Monte Carlo approach [T. Dornheim et al., accepted for publication in J. Chem Phys., arXiv:1508.03221]. The combination of both approaches is able to yield ab initio data for the UEG over the entire density range, above a temperature of about one half of the Fermi temperature. Comparison with restricted path integral Monte Carlo data [E. W. Brown et al., Phys. Rev. Lett. 110, 146405 (2013)] allows us to quantify the systematic error arising from the free particle nodes.