Department of Physics, Imperial College London, London SW7 2AZ, United Kingdom.
Department of Physics, University of Oxford, Oxford OX1 3PU, United Kingdom.
Phys Rev Lett. 2023 Jan 20;130(3):036401. doi: 10.1103/PhysRevLett.130.036401.
Deep neural networks have been very successful as highly accurate wave function Ansätze 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 converges on the translationally invariant ground state at high density and spontaneously breaks the symmetry to produce the crystalline ground state at low density, despite being given no a priori knowledge that a phase transition exists.
深度神经网络作为变分蒙特卡罗计算分子基态的高度精确波函数方法已经非常成功。我们提出了一种这样的方法——费米网（FermiNet）的扩展，用于周期性哈密顿量基态的计算，并研究了均匀电子气。费米网（FermiNet）对小电子气系统基态能量的计算与先前的引发全组态相互作用量子蒙特卡罗（full configuration interaction quantum Monte Carlo，简称 FCIQMC）和扩散蒙特卡罗（diffusion Monte Carlo，简称 DMC）计算结果非常吻合。我们研究了自旋极化均匀电子气，并证明相同的神经网络架构能够准确地表示非局域的费米液体态和局域的维格纳晶体态。尽管没有先验知识表明存在相变，但在高密度下，网络收敛于平移不变的基态，并自发地打破对称性，在低密度下产生晶体基态。
