Synergy between deep neural networks and the variational Monte Carlo method for small $^4He_N$ clusters

TL;DR

This paper presents a neural network-based method combined with variational Monte Carlo to accurately model and analyze small $^4He_N$ clusters, achieving results comparable to diffusion Monte Carlo methods.

Contribution

It introduces a neural network approach for wave functions satisfying Bose-Einstein statistics, demonstrating its effectiveness for small helium clusters.

Findings

Accurately predicts ground state energies of $^4He_N$ clusters.

Matches results of diffusion Monte Carlo within statistical uncertainties.

Provides detailed pair density functions and contact parameters.

Abstract

We introduce a neural network-based approach for modeling wave functions that satisfy Bose-Einstein statistics. Applying this model to small $^4He_N$ clusters (with N ranging from 2 to 14 atoms), we accurately predict ground state energies, pair density functions, and two-body contact parameters $C^{(N)}_2$ related to weak unitarity. The results obtained via the variational Monte Carlo method exhibit remarkable agreement with previous studies using the diffusion Monte Carlo method, which is considered exact within its statistical uncertainties. This indicates the effectiveness of our neural network approach for investigating many-body systems governed by Bose-Einstein statistics.