Understanding superfluidity remains a major goal of condensed matter physics. Here we tackle this challenge utilizing the recently developed Fermionic neural network (FermiNet) wave function Ansatz [D. Pfau et al., Phys. Rev. Res. 2, 033429 (2020).] for variational Monte Carlo calculations. We study the unitary Fermi gas, a system with strong, short-range, two-body interactions known to possess a superfluid ground state but difficult to describe quantitatively. We demonstrate key limitations of the FermiNet Ansatz in studying the unitary Fermi gas and propose a simple modification based on the idea of an antisymmetric geminal power singlet (AGPs) wave function. The new AGPs FermiNet outperforms the original FermiNet significantly in paired systems, giving results which are more accurate than fixed-node diffusion Monte Carlo and are consistent with experiment. We prove mathematically that the new Ansatz, which only differs from the original Ansatz by the method of antisymmetrization, is a strict generalization of the original FermiNet architecture, despite the use of fewer parameters. Our approach shares several advantages with the original FermiNet: the use of a neural network removes the need for an underlying basis set; and the flexibility of the network yields extremely accurate results within a variational quantum Monte Carlo framework that provides access to unbiased estimates of arbitrary ground-state expectation values. We discuss how the method can be extended to study other superfluids.

翻译：理解超流体性质仍然是凝聚态物理学的核心目标之一。本文利用近期发展的费米子神经网络（FermiNet）波函数拟设[D. Pfau et al., Phys. Rev. Res. 2, 033429 (2020)]，通过变分蒙特卡洛计算应对这一挑战。我们研究具有强短程二体相互作用的幺正费米气体——该系统已知存在超流基态但难以进行定量描述。我们揭示了FermiNet拟设在研究幺正费米气体时的关键局限性，并基于反对称双粒子幂单重态（AGPs）波函数思想提出了简易改进方案。新型AGPs FermiNet在配对体系中表现显著优于原始FermiNet，其计算结果比固定节点扩散蒙特卡洛方法更精确，且与实验数据吻合。我们通过数学证明，新拟设仅通过反对称化方法的改进，就成为原始FermiNet架构的严格推广形式，尽管使用了更少的参数。我们的方法继承了原始FermiNet的多重优势：神经网络的使用消除了对基函数集的依赖；网络的灵活性在变分量子蒙特卡洛框架内产生了极高精度的结果，该框架可提供任意基态期望值的无偏估计。我们进一步探讨了该方法在其它超流体体系中的扩展应用前景。