Real-time description of excitons with time-dependent density-functional theory

Time-dependent density-functional theory (TDDFT) is a computationally efficient first-principles approach for calculating optical spectra in insulators and semiconductors, including excitonic effects. We show how excitons can be obtained from real-time TDDFT by propagating the time-dependent Kohn-Sham equation using an exchange-correlation potential with long-range electron-hole interactions. Using an implementation in the Qb@ll code, we demonstrate for various small- and large-gap materials that this approach is not only consistent with frequency-dependent linear response, but also gives access to excitonic effects in the short-pulse and nonlinear regime.