A fast low-rank inversion algorithm of dielectric matrix in GW approximation
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arXiv
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| Auteurs principaux: | , , , , , , |
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| Format: | Preprint |
| Publié: |
2024
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| _version_ | 1866911914470146048 |
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| author | Zhou, Zhengbang Ma, Huanhuan Wu, Wentiao Gao, Weiguo Yang, Jinlong Shao, Meiyue Hu, Wei |
| author_facet | Zhou, Zhengbang Ma, Huanhuan Wu, Wentiao Gao, Weiguo Yang, Jinlong Shao, Meiyue Hu, Wei |
| contents | The dielectric response function and its inverse are crucial physical quantities in materials science. We propose an accurate and efficient strategy to invert the dielectric function matrix. The GW approximation, a powerful approach to accurately describe many-body excited states, is taken as an application to demonstrate accuracy and efficiency. We incorporate the interpolative separable density fitting (ISDF) algorithm with Sherman--Morrison--Woodbury (SMW) formula to accelerate the inversion process by exploiting low-rank properties of dielectric function in plane-wave GW calculations. Our ISDF--SMW strategy produces accurate quasiparticle energies with $O(N_{\mathrm{r}}N_{\mathrm{e}}^2)$ computational cost $(N_{\mathrm{e}}$ is the number of electrons and $N_{\mathrm{r}}=100$--$1000N_{\mathrm{e}}$ is the number of grid points) with negligible small error of $0.03$ eV for both complex molecules and solids. This new strategy for inverting the dielectric matrix can be \(50\times\) faster than the current state-of-the-art implementation in BerkeleyGW, resulting in two orders of magnitude speedup for total GW calculations. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2403_12340 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | A fast low-rank inversion algorithm of dielectric matrix in GW approximation Zhou, Zhengbang Ma, Huanhuan Wu, Wentiao Gao, Weiguo Yang, Jinlong Shao, Meiyue Hu, Wei Numerical Analysis G.1.3; J.2 The dielectric response function and its inverse are crucial physical quantities in materials science. We propose an accurate and efficient strategy to invert the dielectric function matrix. The GW approximation, a powerful approach to accurately describe many-body excited states, is taken as an application to demonstrate accuracy and efficiency. We incorporate the interpolative separable density fitting (ISDF) algorithm with Sherman--Morrison--Woodbury (SMW) formula to accelerate the inversion process by exploiting low-rank properties of dielectric function in plane-wave GW calculations. Our ISDF--SMW strategy produces accurate quasiparticle energies with $O(N_{\mathrm{r}}N_{\mathrm{e}}^2)$ computational cost $(N_{\mathrm{e}}$ is the number of electrons and $N_{\mathrm{r}}=100$--$1000N_{\mathrm{e}}$ is the number of grid points) with negligible small error of $0.03$ eV for both complex molecules and solids. This new strategy for inverting the dielectric matrix can be \(50\times\) faster than the current state-of-the-art implementation in BerkeleyGW, resulting in two orders of magnitude speedup for total GW calculations. |
| title | A fast low-rank inversion algorithm of dielectric matrix in GW approximation |
| topic | Numerical Analysis G.1.3; J.2 |
| url | https://arxiv.org/abs/2403.12340 |