Efficient evaluation of the $k$-space second Chern number in four dimensions
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arXiv
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| Main Authors: | , , , , |
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| Format: | Preprint |
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2026
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| _version_ | 1866911548338864128 |
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| author | Liu, Xiang Yi, Xiao-Xia Liu, Zheng-Rong Chen, Rui Zhou, Bin |
| author_facet | Liu, Xiang Yi, Xiao-Xia Liu, Zheng-Rong Chen, Rui Zhou, Bin |
| contents | We propose an efficient numerical method to compute the $k$-space second Chern number in four-dimensional (4D) topological systems. Our approach employs an adaptive mesh refinement scheme to evaluate the Brillouin-zone integral, which automatically increases the grid density in regions where the Berry curvature is sharply peaked. We compare our method with the 4D lattice-gauge extension of the Fukui-Hatsugai-Suzuki method and a direct uniform grid integration scheme. Compared with these approaches, our method (i) achieves the same accuracy with substantially fewer diagonalizations, and thus runs faster; (ii) requires minimal memory to execute, enabling calculations for larger systems; and (iii) remains accurate even near topological phase transitions where conventional methods often face challenges. These results demonstrate that the adaptive subdivision strategy is a practical and powerful tool for calculating the $k$-space second Chern number. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2603_26505 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Efficient evaluation of the $k$-space second Chern number in four dimensions Liu, Xiang Yi, Xiao-Xia Liu, Zheng-Rong Chen, Rui Zhou, Bin Mesoscale and Nanoscale Physics We propose an efficient numerical method to compute the $k$-space second Chern number in four-dimensional (4D) topological systems. Our approach employs an adaptive mesh refinement scheme to evaluate the Brillouin-zone integral, which automatically increases the grid density in regions where the Berry curvature is sharply peaked. We compare our method with the 4D lattice-gauge extension of the Fukui-Hatsugai-Suzuki method and a direct uniform grid integration scheme. Compared with these approaches, our method (i) achieves the same accuracy with substantially fewer diagonalizations, and thus runs faster; (ii) requires minimal memory to execute, enabling calculations for larger systems; and (iii) remains accurate even near topological phase transitions where conventional methods often face challenges. These results demonstrate that the adaptive subdivision strategy is a practical and powerful tool for calculating the $k$-space second Chern number. |
| title | Efficient evaluation of the $k$-space second Chern number in four dimensions |
| topic | Mesoscale and Nanoscale Physics |
| url | https://arxiv.org/abs/2603.26505 |