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

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.