Subspace Embedding and Downfolding Techniques for Solving the Bethe Salpeter Equation: Interplay of Localized and Continuum Excitons in Complex Systems

Ab initio many-body perturbation theory methods, like GW and GW plus Bethe Salpeter Equation (GW-BSE), are well-established and highly-accurate techniques for calculating the quasiparticle and optical properties of moderate-sized systems. There remain, however, a number of challenges when it comes to scaling up these techniques to address systems with a large number of heterogeneous atoms, various forms of aperiodicity, and large energy scales well-outside the optical regime. In this talk, I will discuss our newly developed subspace embedding and downfolding techniques for GW-BSE calculations on low-dimensional, nanostructured and amorphous systems that exemplify these challenges. In particular, we apply GW-BSE to study optical properties of heterostructures, defects, and molecular functionalization of quasi two-dimensional (quasi-2D) materials. I will also discuss the effect of electron-hole interactions on core-level spectra of quasi-2D materials and amorphous water, including dynamical effects due to scattering with the electron-hole continuum, where we find that electron-hole interactions play an essential role in the scattering of core-level excitations with excitations from the valence band. The calculations are made possible through a combination of physically motivated approximations and algorithms, including non-uniform spatial sampling, low-rank approximations, and subspace embedding and matrix downfolding techniques.