Extending a Lanczos method for real-space GW calculations to periodic systems

The GW approximation provides an accurate modeling for single-particle excitations. Previously, we demonstrated a Lanczos-based approach for full-frequency GW calculations in real space, which can handle confined systems with thousands of atoms. However, for periodic systems, the Casida equation matrix is non-Hermitian and therefore not directly applicable to the Lanczos method. We will discuss a modified Lanczos approach for full-frequency GW calculations in real space for periodic systems, including the application of Tamm-Dancoff Approximation and k-point sampling. This development will enable the study of various periodic systems.