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 \textit{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.

5+2 pages, 6+4 figures

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• Entanglement Transition and Replica Wormhole in the Dissipative Sachdev-Ye-Kitaev Model
• Toward a classification of PT-symmetric quantum systems: From dissipative dynamics to topology and wormholes
• Anatomy of information scrambling and decoherence in the integrable Sachdev-Ye-Kitaev model
• Out-of-time-order correlators for Swanson Hamiltonian with interaction terms