Gao Weiwei, Tang Zhao, Zhao Jijun, Chelikowsky James R
Key Laboratory of Materials Modification by Laser, Ion and Electron Beams, Ministry of Education, Dalian University of Technology, Dalian 116024, China.
Center for Computational Materials, Oden Institute for Computational Engineering and Sciences, The University of Texas at Austin, Austin, Texas 78712, USA.
Phys Rev Lett. 2024 Mar 22;132(12):126402. doi: 10.1103/PhysRevLett.132.126402.
The GW approximation is widely used for reliable and accurate modeling of single-particle excitations. It also serves as a starting point for many theoretical methods, such as its use in the Bethe-Salpeter equation (BSE) and dynamical mean-field theory. However, full-frequency GW calculations for large systems with hundreds of atoms remain computationally challenging, even after years of efforts to reduce the prefactor and improve scaling. We propose a method that reformulates the correlation part of the GW self-energy as a resolvent of a Hermitian matrix, which can be efficiently and accurately computed using the standard Lanczos method. This method enables full-frequency GW calculations of material systems with a few hundred atoms on a single computing workstation. We further demonstrate the efficiency of the method by calculating the defect-state energies of silicon quantum dots with diameters up to 4 nm and nearly 2,000 silicon atoms using only 20 computational nodes.
GW近似被广泛用于单粒子激发的可靠且精确的建模。它也是许多理论方法的起点，比如在贝叶斯 - 萨尔皮特方程（BSE）和动态平均场理论中的应用。然而，即使经过多年努力来降低前置因子并改善缩放比例，对于包含数百个原子的大型系统进行全频GW计算在计算上仍然具有挑战性。我们提出了一种方法，将GW自能的关联部分重新表述为厄米矩阵的预解式，这可以使用标准的兰索斯方法高效且精确地计算。该方法能够在单个计算工作站上对包含几百个原子的材料系统进行全频GW计算。我们通过仅使用20个计算节点来计算直径达4纳米且包含近2000个硅原子的硅量子点的缺陷态能量，进一步证明了该方法的效率。
