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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2026
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2601.12098 |
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| _version_ | 1866915736991039488 |
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| author | Zhang, Zichong Zhu, Shuze |
| author_facet | Zhang, Zichong Zhu, Shuze |
| contents | The exploration of quantum phenomena in complex materials such as moiré superlattices is limited by the O(N^3) scaling of conventional electronic structure methods. Here we introduce a high-performance tight-binding framework that reduces the complexity to O(N^1.5) by transforming the Hamiltonian into a real symmetric form and combining Sylvester's inertia law with LDL decomposition. This approach enables efficient band structure calculations for large systems: solving magic angle twisted bilayer graphene in minutes on a laptop and scaling to 1.5 million atoms within days on a workstation. We apply it to the previously inaccessible ultra-low twist-angle regime (less than 0.16 degree) with mechanical strain relaxation and find robust flat bands persisting down to 0.09 degree. Our framework bridges density functional theory accuracy with large-scale quantum simulation, opening a route to systematic data-driven exploration of mesoscale quantum materials. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2601_12098 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Efficient O(N^1.5) Electronic Structure Computation of Million-Atom Systems Zhang, Zichong Zhu, Shuze Computational Physics Mesoscale and Nanoscale Physics The exploration of quantum phenomena in complex materials such as moiré superlattices is limited by the O(N^3) scaling of conventional electronic structure methods. Here we introduce a high-performance tight-binding framework that reduces the complexity to O(N^1.5) by transforming the Hamiltonian into a real symmetric form and combining Sylvester's inertia law with LDL decomposition. This approach enables efficient band structure calculations for large systems: solving magic angle twisted bilayer graphene in minutes on a laptop and scaling to 1.5 million atoms within days on a workstation. We apply it to the previously inaccessible ultra-low twist-angle regime (less than 0.16 degree) with mechanical strain relaxation and find robust flat bands persisting down to 0.09 degree. Our framework bridges density functional theory accuracy with large-scale quantum simulation, opening a route to systematic data-driven exploration of mesoscale quantum materials. |
| title | Efficient O(N^1.5) Electronic Structure Computation of Million-Atom Systems |
| topic | Computational Physics Mesoscale and Nanoscale Physics |
| url | https://arxiv.org/abs/2601.12098 |