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 $r_{\text{s}}=86.6\left(7\right)$, with no region of stability for an itinerant ferromagnetic fluid.

中文翻译：

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三维电子气的低密度相图

变分和扩散量子蒙特卡罗方法被用来研究极低密度的三维均匀电子气的零温度相图。费米流体和体心立方维格纳晶体基态能量是使用有限模拟单元中不同密度和自旋极化的 Slater-Jastrow 回流和 Slater-Jastrow 多体波函数确定的。使用扭曲平均边界条件和将每个粒子的能量外推到无限系统尺寸的热力学极限来消除有限尺寸误差。与之前的研究不同，我们的研究结果表明，电子气在密度参数下直接从顺磁流体经历一级量子相变到体心立方晶体。$r_{\text{s}}=86.6\left(7\right)$，对于流动的铁磁流体没有稳定区域。