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

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× 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.