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 differs from the original Ansatz only 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; sand 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 superfluid.

中文翻译：

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超流体的神经波函数


理解超流性仍然是凝聚态物理学的一个主要目标。在这里，我们利用最近开发的费米神经网络 (FermiNet) 波函数 Ansatz [D. Pfau 等人，物理学。修订版研究。 2, 033429 (2020).] 用于变分蒙特卡罗计算。我们研究单一费米气体，这是一种具有强、短程、二体相互作用的系统，已知具有超流体基态，但难以定量描述。我们证明了 FermiNet Ansatz 在研究酉费米气体方面的关键局限性，并提出了基于反对称孪子幂单线态 (AGP) 波函数思想的简单修改。新的AGP FermiNet在配对系统中显着优于原始FermiNet，给出的结果比固定节点扩散蒙特卡罗更准确，并且与实验一致。我们从数学上证明，新的 Ansatz 与原始 Ansatz 的区别仅在于反对称化方法，尽管使用了较少的参数，但它是原始 FermiNet 架构的严格泛化。我们的方法与原始 FermiNet 具有以下几个优点：使用神经网络消除了对底层基础集的需求；网络的灵活性在变分量子蒙特卡罗框架内产生极其准确的结果，该框架提供对任意基态期望值的无偏估计。我们讨论了如何将该方法扩展到其他超流体的研究。