Excitonic effects in time-dependent density functional theory from zeros of the density response

We show that the analytic structure of the dynamical exchange-correlation (xc) kernels of semiconductors and insulators can be sensed in terms of its poles, which mark physically relevant frequencies of the system where the counterphase motion of discrete collective excitations occurs: If excited, the collective modes counterbalance each other, making the system exhibit none at all or extremely weak density response. This property can be employed to construct simple and practically relevant approximations of the dynamical xc kernel for time-dependent density functional theory (TDDFT). Such kernels have simple analytic structures, are able to reproduce dominant excitonic features of the absorption spectra of monolayer semiconductors and bulk solids, and promise high potential for future uses in efficient real-time calculations with TDDFT.