Analysis of Dirac exceptional points and their isospectral Hermitian counterparts

Recently, a Dirac exceptional point (EP) was reported in non-Hermitian system. Unlike Hermitian systems, this EP has coalesced eigenstates addition to the degenerate energy. Also different from typical EP, two energy levels connected at remain real its vicinity and display linear instead of square root dispersion, forming tilted cone hybrid space consisting momentum dimension synthetic for strength non-Hermiticity. In report, we first present simple three-band two-band matrix models with where dispersion can be expressed analytically. Importantly, our analysis also reveals that there exist systems have same (real-valued) spectrum their entire parameter space, exception one or more degeneracies former are replaced by EPs later. Finally, show existence an imaginary center.