Hilbert-Space Separation Schemes in Energy-Space and Real-Space for Excited-State Calculations

We discuss two new Hilbert-space separation schemes for GW and GW plus Bethe Salpeter equation (GW-BSE) calculations. In the first, we look at a technique for accelerating calculations on layered metal halide perovskites. In recent years, a number of techniques have been developed to separately calculate the polarizability of systems where the wavefunction overlap is small, such as in layered van der Waals materials or molecules adsorbed on surfaces. Here, we develop a generalized scheme to extend these techniques to systems, such as halide perovskites, where the two subsystems are ionically bonded. We show that this technique can decrease the computational cost of calculations on a single perovskite unit cell by as much as an order of magnitude and is trivially extendable to calculations over larger supercells. In the second scheme, we develop a Hilbert-space downfolding technique for systems where subspaces are well-separated in energy space. We apply this to study shallow core-level excitations in bulk and monolayer transition metal dichalcogenides (TMDs). We find that the typical truncation of the Hilbert space into core and valence levels can give rise to spurious plasmon-like features, whose origin we analyze.