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 bodycentered cubic Wigner crystal ground-state energies are determined using Slater-Jastrow-backflow and SlaterJastrow many-body wave functions at different densities and spin polarizations in finite simulation cells. Finitesize 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 rs = 86.6(7), with no region of stability for an itinerant ferromagnetic fluid.