  Real-time, time-dependent density functional theory (RT-TDDFT) has gained
popularity as a first-principles approach to study a variety of excited-state
phenomena such as optical excitations and electronic stopping. Within RT-TDDFT
simulations, the gauge freedom of the time-dependent electronic orbitals can be
exploited for numerical and scientific convenience while the unitary
transformation does not alter physical properties calculated from the quantum
dynamics of electrons. Exploiting this gauge freedom, we demonstrate
propagation of maximally localized Wannier functions within RT-TDDFT. We
illustrate its great utility through a number of examples including its
application to optical excitation in extended systems using the so-called
length gauge, interpreting electronic stopping excitation, and simulating
electric field-driven quantized charge transport. We implemented the approach
within our plane-wave pseudopotential RT-TDDFT module of the QB@LL code, and
performance of the implementation is also discussed.
