Studying the Superfluid Ground-State of the Unitary Fermi Gas with Fermionic Neural Networks.

Understanding the properties of superfluidity has been a major challenge in condensed matter physics. Here we propose to tackle this challenge utilizing the recently developed Fermionic neural network Ansatz (FermiNet) for variational Monte Carlo (VMC) calculations, which has been proven successful in molecular systems as well as periodic homogeneous electron gas, often outperforming state-of-the-art methods.

We study the unitary Fermi gas (UFG), a system with strong, short-range two body interactions which possesses a superfluid ground state. We demonstrate key limitations of the FermiNet Ansatz in studying the UFG. We propose a simple modification, which outperforms the original FermiNet by a significant amount and is able to obtain comparable, if not better accuracy than the FN-DMC results using BCS trial wavefunction in the same system. We prove mathematically that this new Ansatz is a strict generalization of the original FermiNet architecture, despite the use of fewer parameters.

Our approach shares several key properties with FermiNet: the use of a neural network removes the need for an underlying basis set and its flexiblity enables extremely accurate ground state estimates within a VMC approach. A key advantage of VMC over DMC is that it provides access to unbiased estimates of expectation values such as the density matrices. The method we present here could be extended to study other s-wave superfluids.