Deep Learning DFT Hamiltonians for Ground and Excited-state Calculations of Complex Materials

Despite the advances in low-order scaling methods, traditional first-principles calculations are typically limited in handling general condensed-matter systems containing fewer than a few tens of thousands of atoms. We will discuss how to overcome this limitation by machine-learning the density-functional theory (DFT) Hamiltonian through introducing the DeepH-pack software. It employs a symmetry-equivariant graph neural network to reduce the cubic scaling of traditional calculations to a strictly linear dependence on the number of atoms, enabling efficient construction of the DFT Hamiltonian. The framework integrates seamlessly with several mainstream ab initio workflows and provides automated modules for structure processing, model training, and property inference. We illustrate how DeepH-pack yields accuracy close to direct first-principles calculations across diverse material systems, including two-dimensional crystals, heterostructures, and defected or disordered materials. Finally, we will discuss a recent effort in utilizing DeepH-pack as a starting point for many-body perturbation theory calculations, showcasing that it can replace standard DFT codes when computing the optical response of moiré heterostructures through the Bethe-Salpeter equation.