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.

翻译：介电响应函数及其逆矩阵是材料科学中的关键物理量。本文提出一种精确高效的介电函数矩阵求逆策略。以能精确描述多体激发态的GW近似作为应用场景，验证该策略的精度与效率。我们结合插值可分离密度拟合（ISDF）算法与Sherman-Morrison-Woodbury（SMW）公式，通过挖掘平面波GW计算中介电函数的低秩特性来加速求逆过程。所提出的ISDF-SMW策略能以$O(N_{\mathrm{r}}N_{\mathrm{e}}^2)$计算复杂度（$N_{\mathrm{e}}$为电子数，$N_{\mathrm{r}}=100$--$1000N_{\mathrm{e}}$为格点数）获得精确准粒子能量，对复杂分子和固体体系的误差均小于$0.03$ eV。这种新型介电矩阵求逆策略比BerkeleyGW中现有先进实现快50倍，从而使整体GW计算加速两个数量级。