Excited-state properties are central to the fundamental understanding of many interesting and important phenomena (such as the optical response) of matter that are also essential to modern technologies - optoelectronics, photovoltaics, photocatalysis, energy conversion devices, etc. In this talk, we discuss the theory and applications of the GW plus Bethe Salpeter equation (GW-BSE) approach to the two-particle excitations and optical properties of interacting many-electron systems. The approach is based on quantum many-body perturbation theory. It provides a powerful tool to the ab initio computation and understanding of the optical and related properties of novel materials and reduced dimensional systems where electron-hole interactions are dominant. Selected examples are given to illustrate the versatility of the method and the underlying physics involved.
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