Deep neural networks have been extremely successful as highly accurate wave function ans\"atze for variational Monte Carlo calculations of molecular ground states. We present an extension of one such ansatz, FermiNet, to calculations of the ground states of periodic Hamiltonians, and study the homogeneous electron gas. FermiNet calculations of the ground-state energies of small electron gas systems are in excellent agreement with previous initiator full configuration interaction quantum Monte Carlo and diffusion Monte Carlo calculations. We investigate the spin-polarized homogeneous electron gas and demonstrate that the same neural network architecture is capable of accurately representing both the delocalized Fermi liquid state and the localized Wigner crystal state. The network is given no \emph{a priori} knowledge that a phase transition exists, but converges on the translationally invariant ground state at high density and spontaneously breaks the symmetry to produce the crystalline ground state at low density.

翻译：深神经网络非常成功, 因为高精确的波函数 as\"atze ans\" 用于对分子地面状态进行可变的蒙特卡洛计算。 我们展示了一个这样的 ansatz, FermiNet, 用于计算定期汉密尔顿人的地面状态和研究同质电子气体。 FermiNet 对小型电子气体系统的地面状态能量的计算与先前的启动者完全配置互动量 蒙特卡洛 以及传播蒙特卡洛 的计算非常一致。 我们调查了旋转极化的同质电子气体, 并证明同一神经网络结构能够准确代表非本地化的Fermi液体状态和本地化的Wigner晶体状态。 网络没有获得关于存在阶段过渡的知识, 但是在高密度和自发性断裂对称以生成低密度晶状地面状态。