  Open quantum systems are a subject of immense interest as their understanding
is crucial in the implementation of modern quantum technologies. In the study
of their dynamics, the role of the initial system-environment correlations is
commonly ignored. In this work, to gain insights into the role of these
correlations, we solve an exactly solvable model of a single two-level system
interacting with a spin environment, with the initial system state prepared by
a suitable unitary operation. By solving the dynamics exactly for arbitrary
system-environment coupling strength while taking into account the initial
system-environment correlations, we show that the effect of the initial
correlations is, in general, very significant and non-trivial. To further
highlight the importance of the initial system-environment correlations, we
also extend our study to investigate the dynamics of the entanglement between
two two-level systems interacting with a common spin environment.
