Equivariant neural network for Green's functions of molecules and materials

TL;DR

This paper introduces an equivariant neural network framework for predicting finite-temperature Green's functions in molecules and materials, enabling accurate electronic property calculations beyond traditional density functional theory.

Contribution

It proposes a novel deep learning approach that predicts self-energy matrices using an equivariant message passing neural network, respecting physical symmetries and properties.

Findings

Accurately predicts Green's functions for molecules and periodic systems.

Provides reliable estimates of energies and densities of states.

Demonstrates effectiveness in benchmark tests.

Abstract

The many-body Green's function provides access to electronic properties beyond density functional theory level in ab inito calculations. In this manuscript, we propose a deep learning framework for predicting the finite-temperature Green's function in atomic orbital space, aiming to achieve a balance between accuracy and efficiency. By predicting the self-energy matrices in Lehmann representation using an equivariant message passing neural network, our method respects its analytical property and the $E(3)$ equivariance. The Green's function is obtained from the predicted self-energy through Dyson equation with target total number of electrons. We present proof-of-concept benchmark results for both molecules and simple periodic systems, showing that our method is able to provide accurate estimate of physical observables such as energy and density of states based on the predicted Green's function.