A highly accurate procedure for computing globally optimal Wannier functions in one-dimensional crystalline insulators
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arXiv
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| Auteurs principaux: | , |
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| Format: | Preprint |
| Publié: |
2024
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| _version_ | 1866917022994006016 |
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| author | Gopal, Abinand Zhang, Hanwen |
| author_facet | Gopal, Abinand Zhang, Hanwen |
| contents | A standard task in solid state physics and quantum chemistry is the computation of localized molecular orbitals known as Wannier functions. In this manuscript, we propose a new procedure for computing Wannier functions in one-dimensional crystalline materials. Our approach proceeds by first performing parallel transport of the Bloch functions using numerical integration. Then a simple analytically computable correction is introduced to yield the optimally localized Wannier function. The resulting scheme is rapidly convergent and is proven to yield real-valued Wannier functions that achieve global optimality. The analysis in this manuscript can also be viewed as a proof of the existence of exponentially localized Wannier functions in one dimension. We illustrate the performance of the scheme by a number of numerical experiments. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2409_04369 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | A highly accurate procedure for computing globally optimal Wannier functions in one-dimensional crystalline insulators Gopal, Abinand Zhang, Hanwen Mathematical Physics Numerical Analysis Computational Physics A standard task in solid state physics and quantum chemistry is the computation of localized molecular orbitals known as Wannier functions. In this manuscript, we propose a new procedure for computing Wannier functions in one-dimensional crystalline materials. Our approach proceeds by first performing parallel transport of the Bloch functions using numerical integration. Then a simple analytically computable correction is introduced to yield the optimally localized Wannier function. The resulting scheme is rapidly convergent and is proven to yield real-valued Wannier functions that achieve global optimality. The analysis in this manuscript can also be viewed as a proof of the existence of exponentially localized Wannier functions in one dimension. We illustrate the performance of the scheme by a number of numerical experiments. |
| title | A highly accurate procedure for computing globally optimal Wannier functions in one-dimensional crystalline insulators |
| topic | Mathematical Physics Numerical Analysis Computational Physics |
| url | https://arxiv.org/abs/2409.04369 |