Low-density Phase Diagram of the Three-Dimensional Electron Gas

Variational and diffusion quantum Monte Carlo methods are employed to investigate the zero-temperature phase diagram of the three-dimensional homogeneous electron gas at very low density. Fermi fluid and body-centered cubic Wigner crystal ground state energies are determined using Slater-Jastrow-backflow and Slater-Jastrow many-body wave functions at different densities and spin polarizations in finite simulation cells. Finite-size errors are removed using twist-averaged boundary conditions and extrapolation of the energy per particle to the thermodynamic limit of infinite system size. Unlike previous studies, our results show that the electron gas undergoes a first-order quantum phase transition directly from a paramagnetic fluid to a body-centered cubic crystal at density parameter $r_\text{s} = 86.6(7)$, with no region of stability for an itinerant ferromagnetic fluid. However there is a possible magnetic phase transition from an antiferromagnetic crystal to a ferromagnetic crystal at $r_\text{s}=93(3)$.