  We investigate theoretically charge migration following prompt double
ionization of a polyatomic molecule (C$_2$H$_4$BrI) and find that for double
ionization, correlation-driven charge migration appears to be particularly
prominent, i.e., we observe exceptionally rich dynamics solely driven by the
electron-electron interaction even in the situation when the electrons are
emitted from outer-valence orbitals. These strongly correlated electron
dynamics are witnessed in the theoretically determined time-resolved transient
absorption cross section. Strikingly, features in the cross section can be
traced back to electron hole populations and time-dependent partial charges and
hence, can be interpreted with surprising ease. Remarkably, by taking advantage
of element specific core-to-valence transitions, the hole population dynamics
can be followed both in time and space. With this, not only do we report the
high relevance of correlation-driven charge migration following double
ionization but our findings also highlight the outstanding role of attosecond
transient absorption spectroscopy (ATAS) as one of the most promising
techniques for monitoring ultrafast electron dynamics in complex molecular
systems.
