Detecting Exceptional Point through Dynamics in Non-Hermitian Systems

Abstract: Non-Hermitian rotation-time reversal (RT)-symmetric spin models possess two distinct phases, the unbroken phase in which the entire spectrum is real and the broken phase which contains complex eigenspectra, thereby indicating a transition point, referred to as an exceptional point. We report that the dynamical quantities, namely short and long time average of Loschmidt echo which is the overlap between the initial and the final states, and the corresponding rate function, can faithfully predict the exceptional point known in the equilibrium scenario. In particular, when the initial state is prepared in the unbroken phase and the system is either quenched to the broken or unbroken phase, we analytically demonstrate that the rate function and the average Loschmidt echo can distinguish between the quench occurred in the broken or the unbroken phase for the nearest-neighbor XY model with uniform and alternating magnetic fields, thereby indicating the exceptional point. Furthermore, we exhibit that such quantities are capable of identifying the exceptional point even in models like the non-Hermitian XYZ model with magnetic field which can only be solved numerically.