Low-Rank Inversion for Single-Node 10,000-Atom Plane-Wave GW Calculations

Zhengbang Zhou; Huanhuan Ma; Wentiao Wu; Weiguo Gao; Jinlong Yang; Meiyue Shao; Wei Hu

doi:10.1103/nh3x-gr87

Low-Rank Inversion for Single-Node 10,000-Atom Plane-Wave GW Calculations

Zhengbang Zhou ^1,*, Huanhuan Ma ², Wentiao Wu ², Weiguo Gao ^1,3,4, Jinlong Yang ^2,5, Meiyue Shao ^3,4,6,†, and Wei Hu ^2,5,‡

¹School of Mathematical Sciences, Fudan University, Shanghai 200433, China
²State Key Laboratory of Precision and Intelligent Chemistry, and Hefei National Laboratory, University of Science and Technology of China, Hefei, Anhui 230026, China
³School of Data Science, Fudan University, Shanghai 200433, China
⁴Shanghai Key Laboratory for Contemporary Applied Mathematics, Fudan University, Shanghai 200433, China
⁵MOE Key Laboratory for Mathematical Foundations and Applications of Digital Technology, and Anhui Center for Applied Mathematics, University of Science and Technology of China, Hefei, Anhui 230026, China
⁶MOE Key Laboratory for Computational Physical Sciences, Fudan University, Shanghai 200433, China

^*Contact author: zbzhou21@m.fudan.edu.cn
^†Contact author: myshao@fudan.edu.cn
^‡Contact author: whuustc@ustc.edu.cn

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Phys. Rev. Lett. 137, 156401 – Published 8 October, 2026

DOI: https://doi.org/10.1103/nh3x-gr87

Abstract

The GW approximation accurately describes single-particle excitations but is typically limited by high computational complexity and a large prefactor. We develop a low-rank strategy by combining the interpolative separable density fitting method with the Sherman-Morrison-Woodbury formula to efficiently implement GW-family calculations in different approximation frameworks. Our method resolves the bottlenecks of four-center integrals and screened Coulomb interactions in GW calculations, achieving cubic scaling with a small prefactor and delivering over $50 \times$ speedup compared to the berkeleygw implementation within the COHSEX approximation. We perform a GW calculation for a lithium-hydrogen system with 10 648 atoms on a single compute node, demonstrating the feasibility of excited-state simulations for large-scale systems using limited computational resources.

Physical Review Letters

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Low-Rank Inversion for Single-Node 10,000-Atom Plane-Wave GW Calculations

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Low-Rank Inversion for Single-Node 10,000-Atom Plane-Wave GW Calculations

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