Hidden-nucleons neural-network quantum states for the nuclear many-body problem

TL;DR

This paper introduces a generalized neural network quantum state model with hidden nucleons, significantly improving expressivity and accuracy in solving the nuclear many-body problem, enabling scalable studies of medium-mass nuclei.

Contribution

It extends neural network quantum states to include hidden nucleons, enhancing expressivity and accuracy for nuclear many-body calculations.

Findings

Achieves accuracy comparable to hyperspherical harmonic method in light nuclei.

Matches auxiliary field diffusion Monte Carlo results in $^{16}$O.

Scales polynomially with the number of nucleons, enabling studies of medium-mass nuclei.

Abstract

We generalize the hidden-fermion family of neural network quantum states to encompass both continuous and discrete degrees of freedom and solve the nuclear many-body Schr\"odinger equation in a systematically improvable fashion. We demonstrate that adding hidden nucleons to the original Hilbert space considerably augments the expressivity of the neural-network architecture compared to the Slater-Jastrow ansatz. The benefits of explicitly encoding in the wave function point symmetries such as parity and time-reversal are also discussed. Leveraging on improved optimization methods and sampling techniques, the hidden-nucleon ansatz achieves an accuracy comparable to the numerically-exact hyperspherical harmonic method in light nuclei and to the auxiliary field diffusion Monte Carlo in $^{16}$O. Thanks to its polynomial scaling with the number of nucleons, this method opens the way to highly-accurate quantum Monte Carlo studies of medium-mass nuclei.