# Neural Wave Functions for Superfluids

arXiv: https://arxiv.org/abs/2305.06989 · HTML: https://mlsanity.com/paper/2305.06989/

## Key facts

- Cited by 13 papers in the map (data through 14 Oct 2026).
- Builds on 3 of its 43 references that are in the map.
- First posted on arXiv 11 May 2023.

## Builds on (most cited first, 3 of 3)

- [Deep neural network solution of the electronic Schr"odinger equation](https://mlsanity.com/paper/1909.08423/) (2019)
- [Solving the electronic Schr"odinger equation for multiple nuclear geometries with weight-sharing deep neural networks](https://mlsanity.com/paper/2105.08351/) (2021)
- [Explicitly antisymmetrized neural network layers for variational Monte Carlo simulation](https://mlsanity.com/paper/2112.03491/) (2021)

## Built on by (most cited first, 13 of 13)

- [Pairing-based graph neural network for simulating quantum materials](https://mlsanity.com/paper/2311.02143/) (2023)
- [Neural Pfaffians: Solving Many Many-Electron Schr"odinger Equations](https://mlsanity.com/paper/2405.14762/) (2024)
- [Ab-initio variational wave functions for the time-dependent many-electron Schr"odinger equation](https://mlsanity.com/paper/2403.07447/) (2024)
- [Transferable Neural Wavefunctions for Solids](https://mlsanity.com/paper/2405.07599/) (2024)
- [Functional Neural Wavefunction Optimization](https://mlsanity.com/paper/2507.10835/) (2025)
- [On Representing Electronic Wave Functions with Sign Equivariant Neural Networks](https://mlsanity.com/paper/2403.05249/) (2024)
- [Spin-Adapted Neural Network Wavefunctions in Real Space](https://mlsanity.com/paper/2511.01671/) (2025)
- [Sorting Out Quantum Monte Carlo](https://mlsanity.com/paper/2311.05598/) (2023)
- [Benchmarking Simulacra AI's Quantum Accurate Synthetic Data Generation for Chemical Sciences](https://mlsanity.com/paper/2511.07433/) (2025)
- [Revisiting the Broken Symmetry Phase of Solid Hydrogen: A Neural Network Variational Monte Carlo Study](https://mlsanity.com/paper/2512.17703/) (2025)
- [Excited Pfaffians: Generalized Neural Wave Functions Across Structure and State](https://mlsanity.com/paper/2603.14515/) (2026)
- [Fermionic neural Gibbs states](https://mlsanity.com/paper/2512.04663/) (2025)
- [Honeycomb Crystal in a Mass-Asymmetric Electron-Hole Bilayer](https://mlsanity.com/paper/2610.17030/) (2026)

## Abstract (arXiv)

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.