  In open, driven systems where parity-time symmetry is preserved, phenomena
that defy conventional wisdom emerge near exceptional points, promising
advances in photonics. While most studies focus on two-level systems of a
conventional exceptional point, unconventional exceptional points as well as
reentrant phases have been discovered in separate studies of higher-dimensional
phase spaces. In this Letter, we present a minimal, analytical model that
encompasses several key phenomena in higher-dimensional phase spaces, including
reentrant PT phases, higher-order exceptional points, and anisotropic
exceptional points. Using the exact analytical solution, we identify a new
topological index as the unifying origin of these different phenomena. The
simplicity of the model may furthermore facilitate experimental implementations
for enhanced sensing and efficient polariton devices.
