Out-of-time-ordered correlator in non-Hermitian quantum systems
Liang-Jun Zhai, Shuai Yin
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 exceptional point in the states with lowest real parts of Hamiltonian spectra (LRHS), which host the Yang-Lee edge singularity, but also the exceptional point in states with higher real parts of Hamiltonian spectra (HRHS). 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 exceptional point of the LRHS, this oscillation behavior can be described by both the scaling theory of the zero-dimensional ($0\mathrm{D}$) quantum Yang-Lee edge singularity and the scaling theory of the $1\mathrm{D}$ quantum Ising model, while in the long-time stage the OTOC increases exponentially, controlled by the exceptional point of the HRHS. Possible experimental realizations are then discussed.