GPUTB-2:An efficient E(3) network method for learning high-precision orthogonal Hamiltonian
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arXiv
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| Format: | Preprint |
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2026
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| author | Wang, Yunlong Liang, Zhixin Ding, Chi Wang, Junjie Fan, Zheyong Wang, Hui-Tian Xing, Dingyu Sun, Jian |
| author_facet | Wang, Yunlong Liang, Zhixin Ding, Chi Wang, Junjie Fan, Zheyong Wang, Hui-Tian Xing, Dingyu Sun, Jian |
| contents | Although equivariant neural networks have become a cornerstone for learning electronic Hamiltonians, the intrinsic non-orthogonality of linear combinations of atomic orbitals (LCAO) basis sets poses a fundamental challenge. The computational cost of Hamiltonian orthogonalization scales as O(N^3), which severely hinders electronic structure calculations for large-scale systems containing hundreds of thousands to millions of atoms. To address this issue, we develop GPUTB-2, a framework that learns implicitly orthogonality-preserving Hamiltonians by training directly on electronic band structures. Benefiting from an E(3)-equivariant network accelerated by Gaunt tensor product and SO(2) tensor product layers, GPUTB-2 achieves significantly higher accuracy than GPUTB across multiple benchmark systems. Moreover, GPUTB-2 accurately predicts large-scale electronic structures, including transport properties of temperature-perturbed SnSe and the band structures of magic-angle twisted bilayer graphene. By further integrating this framework with the linear-scaling quantum transport (LSQT) method, we investigate the electronic properties of million-atom amorphous graphene and uncover pressure-induced electronic structure transitions in more complex amorphous silicon. Together, these results establish GPUTB-2 as a high-accuracy and scalable approach for predicting orthogonal Hamiltonians. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2601_13656 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | GPUTB-2:An efficient E(3) network method for learning high-precision orthogonal Hamiltonian Wang, Yunlong Liang, Zhixin Ding, Chi Wang, Junjie Fan, Zheyong Wang, Hui-Tian Xing, Dingyu Sun, Jian Materials Science Although equivariant neural networks have become a cornerstone for learning electronic Hamiltonians, the intrinsic non-orthogonality of linear combinations of atomic orbitals (LCAO) basis sets poses a fundamental challenge. The computational cost of Hamiltonian orthogonalization scales as O(N^3), which severely hinders electronic structure calculations for large-scale systems containing hundreds of thousands to millions of atoms. To address this issue, we develop GPUTB-2, a framework that learns implicitly orthogonality-preserving Hamiltonians by training directly on electronic band structures. Benefiting from an E(3)-equivariant network accelerated by Gaunt tensor product and SO(2) tensor product layers, GPUTB-2 achieves significantly higher accuracy than GPUTB across multiple benchmark systems. Moreover, GPUTB-2 accurately predicts large-scale electronic structures, including transport properties of temperature-perturbed SnSe and the band structures of magic-angle twisted bilayer graphene. By further integrating this framework with the linear-scaling quantum transport (LSQT) method, we investigate the electronic properties of million-atom amorphous graphene and uncover pressure-induced electronic structure transitions in more complex amorphous silicon. Together, these results establish GPUTB-2 as a high-accuracy and scalable approach for predicting orthogonal Hamiltonians. |
| title | GPUTB-2:An efficient E(3) network method for learning high-precision orthogonal Hamiltonian |
| topic | Materials Science |
| url | https://arxiv.org/abs/2601.13656 |