Advancing Universal Deep Learning for Electronic-Structure Hamiltonian Prediction of Materials
Shi Yin, Zujian Dai, Xinyang Pan, Lixin He
TL;DR
This work addresses the challenge of universal electronic-structure Hamiltonian prediction across diverse materials, including SOC, by introducing NextHAM: a delta-learning framework that uses zeroth-step Hamiltonians $\mathbf{H}^{(0)}$ derived from initial densities as inputs and predicts the correction $\Delta \mathbf{H}$ with an $E(3)$-equivariant Transformer built upon the TraceGrad paradigm. It jointly optimizes real-space and reciprocal-space quantities to suppress ghost states and ensure consistent band structures, employing an ensemble over interatomic distances and a gauge-invariant loss with a tunable shift $\mu$ to address Hamiltonian gauge freedom. The authors release Materials-HAM-SOC, a 17,000-structure, SOC-inclusive benchmark spanning $>60$ elements, enabling robust generalization tests. Empirically, NextHAM achieves DFT-level Hamiltonian and band-structure accuracy with substantial speedups over traditional DFT, demonstrating strong generalization, including to unseen elements like Neon, and offering a practical pathway for high-throughput materials screening and large-scale simulations.
Abstract
Deep learning methods for electronic-structure Hamiltonian prediction has offered significant computational efficiency advantages over traditional DFT methods, 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 Hamiltonians, 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 for learning. 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. On the dataset side, we curate a high-quality broad-coverage large benchmark, namely Materials-HAM-SOC, comprising 17,000 material structures spanning 68 elements from six rows of the periodic table and explicitly incorporating SOC effects. Experimental results on Materials-HAM-SOC demonstrate that NextHAM achieves excellent accuracy and efficiency in predicting Hamiltonians and band structures.