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 three-dimensional homogeneous electron gas at very low density. Fermi fluid body-centered cubic Wigner crystal ground-state energies determined using Slater-Jastrow-backflow Slater-Jastrow many-body wave functions different densities spin polarizations in finite simulation cells. Finite-size errors removed twist-averaged boundary conditions extrapolation energy per particle thermodynamic limit infinite system size. Unlike previous studies, our results show that undergoes a first-order transition directly from paramagnetic density parameter ${r}_{\text{s}}=86.6(7)$, with no region stability for an itinerant ferromagnetic fluid.