Towards real-time TDDFT for excitons in solids

Time-dependent density-functional theory (TDDFT) has been established as an accurate and efficient method to simulate real-time electron and spin dynamics in solids from first principles. However, excitonic effects are challenging since standard semilocal exchange-correlation functionals fail to produce the required electron-hole interaction. In linear response, simple long-range corrected (LRC) functionals can qualitatively capture excitonic features in optical spectra; moreover, dielectrically screened hybrid functionals achieve excellent agreement with the Bethe-Salpeter equation at a fraction of the computational cost. Here we discuss, for a two-dimensional model solid, how these approaches carry over to the real-time domain and into the nonlinear, ultrafast regime. Two important issues will be highlighted: the numerical stability of the LRC functionals and the implementation of hybrid functionals with time-dependent screening. We also show how TDDFT can conveniently visualize time-dependent exciton wave functions. This opens up new opportunities for simulating exciton dynamics in a wide range of materials.