Advancing Universal Deep Learning for Electronic-Structure Hamiltonian Prediction of Materials

Deep learning methods for electronic-structure Hamiltonian prediction has offered significant computational efficiency advantages over traditional density functional theory (DFT), yet the diversity of atomic types, structural patterns, and the high-dimensional complexity of Hamiltonians pose substantial challenges to the generalization performance. In this work, we contribute on both the methodology and dataset sides to advance universal deep learning paradigm for Hamiltonian prediction. On the method side, we propose NextHAM, a neural E(3)-symmetry and expressive correction method for efficient and generalizable materials electronic-structure Hamiltonian prediction. First, we introduce the zeroth-step Hamiltoni-ans, which can be efficiently constructed by the initial charge density of DFT, as informative descriptors of neural regression model in the input level and initial estimates of the target Hamiltonian in the output level, so that the regression model directly predicts the correction terms to the target ground truths, thereby significantly simplifying the input-output mapping and facilitating fine-grained predictions. Second, we present a neural Transformer architecture with strict E(3)-Symmetry and high non-linear expressiveness for Hamiltonian prediction. Third, we propose a novel training objective to ensure the accuracy performance of Hamiltonians in both real space and reciprocal space, preventing error amplification and the occurrence of "ghost states" caused by the large condition number of the overlap matrix. Experimental results on Materials-HAM-SOC demonstrate that NextHAM achieves excellent accuracy in predicting Hamiltonians and band structures, with spin-off-diagonal block reaching the accuracy of sub-µeV scale. These results establish NextHAM as a universal and highly accurate deep learning model for electronic-structure prediction, delivering DFT -level precision with dramatically improved computational efficiency. Understanding the electronic structure is fundamental to unraveling how electrons govern the properties of condensed matter systems. This knowledge is essential for predicting a wide range of material characteristics, such as electrical conductivity, magnetism, optical behavior, and chemical activity, which are vital for technologies spanning from electronics to sustainable energy and advanced catalysis. At the heart of these calculations is the challenge of determining the system's Hamiltonian matrix, whose eigenvalues and eigenstates yield important quantities like energy levels, band structures, and electronic wavefunctions. Traditionally, Density Functional Theory (DFT) (Hohenberg & Kohn, 1964; Kohn & Sham, 1965) has been the standard approach for these problems. Recently, deep learning has emerged as a powerful tool in the physical sciences (Zhang et al., 2025).