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The many-body Green's function provides access to electronic propertiesbeyond density functional theory level in ab inito calculations. In thismanuscript, we propose a deep learning framework for predicting thefinite-temperature Green's function in atomic orbital space, aiming to achievea balance between accuracy and efficiency. By predicting the self-energymatrices in Lehmann representation using an equivariant message passing neuralnetwork, our method respects its analytical property and the $E(3)$equivariance. The Green's function is obtained from the predicted self-energythrough Dyson equation with target total number of electrons. We presentproof-of-concept benchmark results for both molecules and simple periodicsystems, showing that our method is able to provide accurate estimate ofphysical observables such as energy and density of states based on thepredicted Green's function.

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