Accurate calculation of Wannier centers, position matrix, and composite operators using translationally equivariant and higher-order finite differences
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arXiv
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| Auteurs principaux: | , , , |
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| Format: | Preprint |
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2026
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| _version_ | 1866913059215245312 |
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| author | Lihm, Jae-Mo Ghim, Minsu Hong, Seung-Ju Park, Cheol-Hwan |
| author_facet | Lihm, Jae-Mo Ghim, Minsu Hong, Seung-Ju Park, Cheol-Hwan |
| contents | The momentum-space derivatives of Bloch wavefunctions are essential for studying quantum geometry and the equilibrium and response properties of solids. In practical first-principles calculations, these derivatives are obtained via Wannier interpolation of position and related composite matrices. These matrices are initially evaluated on a coarse k-point grid using finite-difference approximations and then interpolated to a dense grid. The accuracy of the finite-difference approximation directly impacts the convergence and reliability of the result. In this work, we present two key improvements to the finite-difference calculation of position and composite operators for Wannier interpolation. First, we formulate a translationally equivariant scheme that preserves the underlying symmetries of the system and significantly reduces finite-difference errors. Second, we introduce a higher-order finite-difference approach that yields a more accurate approximation of the k-space derivatives by systematically increasing the convergence rate. From a real-space perspective, these improvements correspond to better approximations of the position operator at the locations of the Wannier functions. We also present a generalization of the finite-difference scheme, which may reduce the number of finite-difference points while maintaining accuracy. We demonstrate the effectiveness of our methods by applying them to the calculation of Wannier centers and spreads, electric polarization, off-diagonal position matrix elements, orbital magnetization, and spin Hall conductivity. Our results demonstrate significant reductions in finite-difference errors, elimination of symmetry-violating errors, and improved convergence with respect to k-point sampling. These methods have been implemented in the open-source packages and can be readily adopted in other Wannier-based codes with minimal computational overhead. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2604_22614 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Accurate calculation of Wannier centers, position matrix, and composite operators using translationally equivariant and higher-order finite differences Lihm, Jae-Mo Ghim, Minsu Hong, Seung-Ju Park, Cheol-Hwan Materials Science The momentum-space derivatives of Bloch wavefunctions are essential for studying quantum geometry and the equilibrium and response properties of solids. In practical first-principles calculations, these derivatives are obtained via Wannier interpolation of position and related composite matrices. These matrices are initially evaluated on a coarse k-point grid using finite-difference approximations and then interpolated to a dense grid. The accuracy of the finite-difference approximation directly impacts the convergence and reliability of the result. In this work, we present two key improvements to the finite-difference calculation of position and composite operators for Wannier interpolation. First, we formulate a translationally equivariant scheme that preserves the underlying symmetries of the system and significantly reduces finite-difference errors. Second, we introduce a higher-order finite-difference approach that yields a more accurate approximation of the k-space derivatives by systematically increasing the convergence rate. From a real-space perspective, these improvements correspond to better approximations of the position operator at the locations of the Wannier functions. We also present a generalization of the finite-difference scheme, which may reduce the number of finite-difference points while maintaining accuracy. We demonstrate the effectiveness of our methods by applying them to the calculation of Wannier centers and spreads, electric polarization, off-diagonal position matrix elements, orbital magnetization, and spin Hall conductivity. Our results demonstrate significant reductions in finite-difference errors, elimination of symmetry-violating errors, and improved convergence with respect to k-point sampling. These methods have been implemented in the open-source packages and can be readily adopted in other Wannier-based codes with minimal computational overhead. |
| title | Accurate calculation of Wannier centers, position matrix, and composite operators using translationally equivariant and higher-order finite differences |
| topic | Materials Science |
| url | https://arxiv.org/abs/2604.22614 |