  We find the geometric phase of a two-level system undergoing pure dephasing
via interaction with an arbitrary environment, taking into account the effect
of the initial system-environment correlations. We use our formalism to
calculate the geometric phase for the two-level system in the presence of both
harmonic oscillator and spin environments, and we consider the initial state of
the two-level system to be prepared by a projective measurement or a unitary
operation. The geometric phase is evaluated for a variety of parameters such as
the system-environment coupling strength to show that the initial correlations
can affect the geometric phase very significantly even for weak and moderate
system-environment coupling strengths. Moreover, the correction to the
geometric phase due to the system-environment coupling generally becomes
smaller (and can even be zero) if initial system-environment correlations are
taken into account, thus implying that the system-environment correlations can
increase the robustness of the geometric phase.
