Efficient time-dependent Wannier functions for ultrafast dynamics

Time-dependent Wannier functions were initially proposed as a means for calculating the polarization current in crystals driven by external fields. In this work, we present a simple gauge where Wannier states are defined based on the maximally localized functions at the initial time, and are propagated using the time-dependent Bloch states obtained from established first-principles calculations, avoiding the costly Wannierization at each time step. We show that this basis efficiently describes the time-dependent polarization of the laser-driven system through the analysis of the motion of Wannier centers. We use this technique to analyze highly nonlinear and nonperturbative responses such as high-harmonic generation in solids, using hexagonal boron nitride as an illustrative example, and we show how it provides an intuitive picture for the physical mechanisms.