Message-Passing Neural Quantum States for the Homogeneous Electron Gas

TL;DR

This paper presents a message-passing neural network wave function Ansatz that efficiently simulates the homogeneous electron gas, accurately capturing ground states with fewer parameters and enabling larger system sizes.

Contribution

Introduction of a novel message-passing neural network Ansatz for quantum states that embeds symmetry constraints and scales to larger electron systems in continuous space.

Findings

Achieves accurate ground-state energies with fewer parameters.

Scales to 128 electrons, surpassing previous neural network methods.

Capable of representing different phases of matter.

Abstract

We introduce a message-passing-neural-network-based wave function Ansatz to simulate extended, strongly interacting fermions in continuous space. Symmetry constraints, such as continuous translation symmetries, can be readily embedded in the model. We demonstrate its accuracy by simulating the ground state of the homogeneous electron gas in three spatial dimensions at different densities and system sizes. With orders of magnitude fewer parameters than state-of-the-art neural-network wave functions, we demonstrate better or comparable ground-state energies. Reducing the parameter complexity allows scaling to $N=128$ electrons, previously inaccessible to neural-network wave functions in continuous space, enabling future work on finite-size extrapolations to the thermodynamic limit. We also show the Ansatz's capability of quantitatively representing different phases of matter.