Topologically protected exceptional points and reentrant PT phase in an exact ternary model

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 article, 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 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.