Out-of-time-ordered correlator in non-Hermitian quantum systems

TL;DR

This paper investigates how out-of-time-ordered correlators (OTOCs) can diagnose exceptional points in non-Hermitian quantum Ising systems, revealing distinct dynamical behaviors near these points and proposing experimental setups.

Contribution

It demonstrates that OTOCs can identify both ground state and dynamical exceptional points in non-Hermitian systems, linking their behavior to known scaling theories.

Findings

OTOC oscillates periodically in short-time regime near exceptional points

Exponential growth of OTOC occurs in long-time regime controlled by dynamical exceptional point

Scaling theories of Yang-Lee edge singularity and quantum Ising model describe OTOC behavior

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.