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.
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