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Transmission phase lapse in the non-Hermitian Aharonov-Bohm interferometer near the spectral singularity

We study the effect of PT-symmetric imaginary potentials embedded in the two arms of an Aharonov-Bohm interferometer on the transmission phase by finding an exact solution for a concrete tight-binding system. It is observed that the spectral singularity always occurs at k=${\pm}$π/2 for a wide range of fluxes and imaginary potentials. Critical behavior associated with the physics of the spectral singularity is also investigated. It is demonstrated that the quasi-spectral singularity corresponds to a transmission maximum and the transmission phase jumps abruptly by π when the system is swept through this point. Moreover, We find that there exists a pulse-like phase lapse when the imaginary potential approaches the boundary value of the spectral singularity.