Neural Quantum States for Light Nuclei with Chiral Two- and Three-Body Interactions

Abstract

Finding high-quality trial wave functions for quantum Monte Carlo calculations of light nuclei requires a strong intuition for modeling the interparticle correlations as well as large computational resources for exploring the space of variational parameters. Moreover, for systems with three-body interactions, the wave function should account for many-body effects beyond simple pairwise correlations. In this work, we design neural networks that efficiently incorporate these factors to generate expressive wave function Ansätze for light nuclei using variational Monte Carlo. Our neural-network approach for $A=3$ nuclei can capture, already at the level of variational Monte Carlo, the overwhelming majority of the ground-state energy estimated by Green's Function Monte Carlo (GFMC). It achieves a ground-state energy within $0.45\%$ of the GFMC result for ${}^3\mathrm{H}$ using the softest chiral interaction, representing a substantial improvement over standard variational Monte Carlo, which exhibits a $3.7\%$ deviation. The result indicates the potential of neural networks to construct effective trial wave functions for quantum Monte Carlo calculations.

Comments: 6 pages, 4 figures