Interconversion of exceptional points between different orders in non-Hermitian systems

Singularities of non-Hermitian systems typified by exceptional points (EPs) are critical for understanding non-Hermitian topological phases and trigger many intriguing phenomena. However, it remains unexplored what happens when EPs meet one another. Here, in a typical four-level model with both touching and crossing intersections of EP hypersurfaces, we report the interconversion mechanisms between EPs of different orders. By examining both the eigenvalues and eigenvectors, we show analytically that all EPs of higher orders are formed at the touching intersections of two different types of EP hypersurfaces of lower orders. Contrarily, the crossing intersection of EP structures lowers the order of EPs. The mechanisms of the increase and decrease in defectiveness discovered here are expected to hold for EPs of any order in various non-Hermitian systems, providing a comprehensive understanding of EPs and inspiration toward advanced applications such as biosensing and information processing.