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arXiv:2609.36962

Deep Learning GW Quasiparticle Hamiltonians for Many-Body Excited-State Electronic Structure at Scale

Xiaoxun Gong, Zechen Tang, Woochang Kim, Yang Li, Wenhui Duan, Yong Xu, Steven G. Louie

Published Sep 29, 2026• 0 citations
arXivHTMLPDF

Abstract

Accurate quasiparticle electronic structures are the foundation for understanding excited-state properties of materials and explaining optoelectronic, quantum, and transport phenomena. First-principles GW calculations nevertheless remain computationally intensive for large or configurationally complex systems. Here we introduce DeepH-GW, a deep-learning framework that predicts an effective GW quasiparticle Hamiltonian directly from atomic structure. Building on the local, equivariant message-passing architecture of DeepH, DeepH-GW is trained on high-fidelity plane-wave GW calculations through a real-space Hamiltonian-reconstruction interface. This approach combines the systematic accuracy and broad chemical applicability of plane-wave methods with linear-scaling neural-network inference. Across the systems examined, DeepH-GW reproduces quasiparticle band structures with errors on the order of a few meV. Moreover, we show that, despite the intrinsic nonlocality of many-body interactions, DeepH-GW exhibits strong cross-scale transferability from relatively small training structures to substantially larger supercells. We demonstrate that the framework can accurately capture GW-level electron-phonon band-gap renormalization through predictions in supercells with thermal displacements, illustrating the power of the approach. DeepH-GW therefore provides a practical route toward large-scale many-body simulations and foundation models for excited-state electronic structure.

DOI
10.48550/arxiv.2609.36962

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Accurate quasiparticle electronic structures are the foundation for understanding excited-state properties of materials and explaining optoelectronic, quantum, and transport phenomena. First-principles GW calculations nevertheless remain computationally intensive for large or configurationally complex systems. Here we introduce DeepH-GW, a deep-learning framework that predicts an effective GW quasiparticle Hamiltonian directly from atomic structure. Building on the local, equivariant message-passing architecture of DeepH, DeepH-GW is trained on high-fidelity plane-wave GW calculations through a real-space Hamiltonian-reconstruction interface. This approach combines the systematic accuracy and broad chemical applicability of plane-wave methods with linear-scaling neural-network inference. Across the systems examined, DeepH-GW reproduces quasiparticle band structures with errors on the order of a few meV. Moreover, we show that, despite the intrinsic nonlocality of many-body interactions, DeepH-GW exhibits strong cross-scale transferability from relatively small training structures to substantially larger supercells. We demonstrate that the framework can accurately capture GW-level electron-phonon band-gap renormalization through predictions in supercells with thermal displacements, illustrating the power of the approach. DeepH-GW therefore provides a practical route toward large-scale many-body simulations and foundation models for excited-state electronic structure.
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Abstract Deep-learning-based variational Monte Carlo has emerged as a highly accurate method for solving the many-electron Schrödinger equation. Despite favorable scaling with the number of electrons, O(nel4){\mathcal{O}}({{n}_{{\rm{el}}}}^{4})O(nel​4) O ( n el 4 ) , the practical value of deep-learning-based variational Monte Carlo is limited by the high cost of optimizing the neural network weights for every system studied. Recent research has proposed optimizing a single neural network across multiple systems, reducing the cost per system. Here we extend this approach to solids, which require numerous calculations across different geometries, boundary conditions and supercell sizes. We demonstrate that optimization of a single ansatz across these variations significantly reduces optimization steps. Furthermore, we successfully transfer a network trained on 2 × 2 × 2 supercells of LiH, to 3 × 3 × 3 supercells, reducing the number of optimization steps required to simulate the large system by a factor of 50 compared with previous work.
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)E(3)E(3) equivariance. The Green's function is obtained from the predicted self-energy through the 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 an accurate estimate of physical observables such as energy and density of states based on the predicted Green's function.
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