Out-of-time-ordered correlator in non-Hermitian quantum systems
Abstract
We study the behavior of the out-of-time-ordered correlator (OTOC) in a non-Hermitian quantum Ising system. We show that the OTOC can diagnose not only the ground state exceptional point, which hosts the Yang-Lee edge singularity, but also the dynamical exceptional point at the excited state. We find that the evolution of the OTOC in the parity-time symmetric phase can be divided into two stages: in the short-time stage, the OTOC oscillates periodically, and when the parameter is near the ground state exceptional point, this oscillation behavior can be described by both the scaling theory of the (0+1)D Yang-Lee edge singularity and the scaling theory of the (1+1)D quantum Ising model; while in the long-time stage the OTOC increases exponentially, controlled by the dynamical exceptional point. Possible experimental realizations are then discussed.