Highly accurate results for the homogeneous electron gas (HEG) have only been achieved to date within a diffusion Monte Carlo (DMC) framework. Here, we introduce a newly developed stochastic technique, Full Configuration Interaction Quantum Monte Carlo (FCIQMC), which samples the exact wavefunction expanded in plane wave Slater determinants. Despite the introduction of a basis set incompleteness error, we obtain a finite-basis energy which is significantly, and variationally lower than any previously published work for the 54-electron HEG at rs = 0.5 a.u., in a Hilbert space of 10108 Slater determinants. At this value of rs, as well as of 1.0 a.u., we remove the remaining basis set incompleteness error by extrapolation, yielding results comparable or better than state-of-the-art DMC backflow energies. In doing so, we demonstrate that it is possible to yield highly accurate results with the FCIQMC method in sizable periodic systems.
@article{arxiv.1109.2635,
title = {A Full Configuration Interaction Perspective on the Homogeneous Electron Gas},
author = {James J. Shepherd and George Booth and Andreas Grüneis and Ali Alavi},
journal= {arXiv preprint arXiv:1109.2635},
year = {2012}
}