Real-Time Exciton Dynamics with Time-Dependent Density-Functional Theory

Linear-response time-dependent density-functional theory (TDDFT) can describe excitonic features in the optical spectra of insulators and semiconductors, using exchange-correlation (xc) kernels behaving as -1/k^{2} to leading order. We show how excitons can be modeled in real-time TDDFT, using an xc vector potential constructed from approximate, long-range corrected xc kernels. We demonstrate, for various materials, that this real-time approach is consistent with frequency-dependent linear response, gives access to femtosecond exciton dynamics following short-pulse excitations, and can be extended with some caution into the nonlinear regime.