Electron-hole interactions in correlated electron materials: Optical properties of vanadium dioxide from first principles

Correlated materials have been studied extensively using photoemission spectroscopy. Their optical properties are instead much less explored. Here we present calculations of the optical absorption spectrum of vanadium dioxide $({\mathrm{VO}}_{2})$ in the framework of the Bethe-Salpeter equation (BSE) of many-body perturbation theory. In order to deal with localized electrons we go beyond the standard BSE implementation and extend it to correlated insulators. We show that it is not enough to describe the spectra on the basis of independent electron-hole pairs, even when the electron and hole are separately well described by state-of-the-art one-body Green's functions. Crystal local-field effects are crucial to explain the experimental findings, even qualitatively, and excitonic effects strongly modify the spectra, especially at their onset. In this context, as highighted by the analysis of the BSE results, the quasi-one-dimensional nature of the vanadium-dimer chains plays a prominent role.