  Quantum walk research has mainly focused on evolutions due to repeated
applications of time-independent unitary coin operators. However, the idea of
controlling the single particle evolution using time-dependent unitary coins
has still been a subject of multiple studies as it not only hosts interesting
possibilities for quantum information processing but also opens a much richer
array of phenomena including static and dynamic localizations. So far, such
studies have been performed only for single quantum walkers. In case of
multi-walker systems, time-dependent coins may generate measurable phenomena
not described by the single-particle model, due to entanglement and interaction
among the walkers. In this context, we present here a thorough numerical study
of an one dimensional system of two quantum walkers exhibiting rich collective
dynamics controlled by simple time-dependent unitary coins proposed in [Phys.
Rev. A \textbf{80}, 042332(2009)] and [Phys. Rev. A \textbf{73},062304(2006)].
We study how the interplay of coin time-dependence, simple interaction schemes,
entanglement and the relative phase between the coin states of the particles
influences the evolution of the quantum walk. The results show that the system
offers a rich variety of collective dynamical behavior while being controlled
by time dependent coins. In particular, we find and characterize fascinating
two-body localization phenomena with tunable quasiperiodic dynamics of
correlations and entanglements which are quantities of quantum origin.
