  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=${\pm}${\pi}/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 {\pi} 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.
