Synergy between deep neural networks and the variational Monte Carlo method for small ${}^{4}H{e}_N$ clusters

Abstract

We introduce a neural network-based approach for modeling wave functions that satisfy Bose-Einstein statistics. Applying this model to small ${}^{4}H{e}_N$ clusters (with N ranging from 2 to 14 atoms), we accurately predict ground state energies, pair density functions, and two-body contact parameters $C_2^{(N)}$ 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.

arXiv comment9 pages, 5 figures

References in corpus (31)

• Solving the Quantum Many-Body Problem with Artificial Neural Networks
• Large momentum part of fermions with large scattering length
• Energetics of a strongly correlated Fermi gas
• Deep neural network solution of the electronic Schrödinger equation
• Ab-Initio Solution of the Many-Electron Schrödinger Equation with Deep Neural Networks
• Optimizing Neural Networks with Kronecker-factored Approximate Curvature
• Generalized Virial Theorem and Pressure Relation for a strongly correlated Fermi gas
• On scientific understanding with artificial intelligence
• General relations for quantum gases in two and three dimensions. Two-component fermions
• NetKet 3: Machine Learning Toolbox for Many-Body Quantum Systems
• Two-dimensional dynamics of expansion of a degenerate Bose gas
• Exact relations for quantum-mechanical few-body and many-body problems with short-range interactions in two and three dimensions
• General relations for quantum gases in two and three dimensions. II. Bosons and mixtures
• Machine learning technique to find quantum many-body ground states of bosons on a lattice
• Imaging the He${}_2$ quantum halo state using a free electron laser
• Four-Body Scale in Universal Few-Boson Systems
• Wave function Ansatz (but Periodic) Networks and the Homogeneous Electron Gas
• Nonlinear Network description for many-body quantum systems in continuous space
• Deep Learning-Enhanced Variational Monte Carlo Method for Quantum Many-Body Physics
• Ground-state properties of unitary bosons: from clusters to matter
• A Self-Attention Ansatz for Ab-initio Quantum Chemistry
• Artificial Neural Networks as Trial Wave Functions for Quantum Monte Carlo
• From few to many bosons inside the unitary window: a transition between universal to non-universal behavior
• Universal Short Range Correlations in Bosonic Helium Clusters
• Weakly parametrized Jastrow ansatz for a strongly correlated Bose system
• The van der Waals interaction as the starting point for an effective field theory
• Non-Universal and Universal Aspects of The Large Scattering Length Limit
• Subleading contributions to $N$-boson systems inside the universal window
• Sampling-free Inference for Ab-Initio Potential Energy Surface Networks
• Universal behavior of few-boson systems using potential models
• Structural properties of bosonic He clusters with N=2-10 for different potential models at the physical point and at unitarity