A fast low-rank inversion algorithm of dielectric matrix in GW approximation
<|reference_start|>A fast low-rank inversion algorithm of dielectric matrix in GW approximation: 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.<|reference_end|>
@article{zhou2024a,
    title={A fast low-rank inversion algorithm of dielectric matrix in GW
  approximation},
    author={Zhengbang Zhou, Huanhuan Ma, Wentiao Wu, Weiguo Gao, Jinlong Yang,
  Meiyue Shao, and Wei Hu},
    journal={arXiv preprint arXiv:2403.12340},
    year={2024},
    archivePrefix={arXiv},
    eprint={2403.12340},
    primaryClass={math.NA cs.NA}
}