Lanczos algorithm for full-frequency GW calculations in real space*

The GW approximation is a reliable and accurate method for modeling single-particle excitations. However, full-frequency GW calculations for large systems remain a computational challenge. We propose a method that reformulates the correlation part of GW self-energy as a resolvent matrix element, which can be effectively computed with Lanczos algorithm. The implementation of this method in NanoGW demonstrates high accuracy and efficiency, enabling us to study systems with a few hundred atoms on a workstation. In a recent benchmark calculation, we employed 20 GPU nodes for full-frequency GW quasiparticle energies of a silicon nanoparticle containing nearly 2,000 atoms.