Wave function Ansatz (but Periodic) Networks and the Homogeneous Electron Gas

TL;DR

This paper introduces a neural network wave function Ansatz for the Homogeneous Electron Gas, achieving high accuracy across various densities and spin states, advancing neural network applications in periodic electronic systems.

Contribution

It extends neural network Ansatz methods to periodic systems, incorporating spin-specific pairwise streams and backflow coordinate generation for improved performance.

Findings

Achieved comparable or higher accuracy than state-of-the-art methods.

Successfully modeled both spin-polarized and paramagnetic phases.

Demonstrated the utility of high-quality wave functions in computing density matrices.

Abstract

We design a neural network Ansatz for variationally finding the ground-state wave function of the Homogeneous Electron Gas, a fundamental model in the physics of extended systems of interacting fermions. We study the spin-polarised and paramagnetic phases with 7, 14 and 19 electrons over a broad range of densities from $r_s=1$ to $r_s=100$, obtaining similar or higher accuracy compared to a state-of-the-art iterative backflow baseline even in the challenging regime of very strong correlation. Our work extends previous applications of neural network Ans\"{a}tze to molecular systems with methods for handling periodic boundary conditions, and makes two notable changes to improve performance: splitting the pairwise streams by spin alignment and generating backflow coordinates for the orbitals from the network. We illustrate the advantage of our high quality wave functions in computing the reduced single particle density matrix. This contribution establishes neural network models as flexible and high precision Ans\"{a}tze for periodic electronic systems, an important step towards applications to crystalline solids.