  Deep-learning electronic structure calculations show great potential for
revolutionizing the landscape of computational materials research. However,
current neural-network architectures are not deemed suitable for widespread
general-purpose application. Here we introduce a framework of equivariant
local-coordinate transformer, designed to enhance the deep-learning density
functional theory Hamiltonian referred to as DeepH-2. Unlike previous models
such as DeepH and DeepH-E3, DeepH-2 seamlessly integrates the simplicity of
local-coordinate transformations and the mathematical elegance of equivariant
neural networks, effectively overcoming their respective disadvantages. Based
on our comprehensive experiments, DeepH-2 demonstrates superiority over its
predecessors in both efficiency and accuracy, showcasing state-of-the-art
performance. This advancement opens up opportunities for exploring universal
neural network models or even large materials models.
