Extended exceptional points in projected non-Hermitian systems

Exceptional points are interesting physical phenomena in non-Hermitian physics at which the eigenvalues are degenerate and the eigenvectors coalesce. In this paper, we find that in projected non-Hermitian two-level systems (sub-systems under projecting partial Hilbert space) the singularities of exceptional points (EPs) is due to basis defectiveness rather than energy degeneracy or state coalescence. This leads to the discovery of extended exceptional points (EEPs). For EEPs, more subtle structures (e.g. the so-called Bloch peach), additional classification, and 'hidden' quantum phase transitions are explored. By using the topologically protected sub-space from two edge states in the non-Hermitian Su-Schrieffer-Heeger model as an example, we illustrate the physical properties of different types of EEPs.