Scaling laws of the out-of-time-order correlators at the transition to the spontaneous $\cal{PT}$-symmetry breaking in a Floquet system

TL;DR

This paper studies how out-of-time-order correlators behave at the transition to spontaneous $ ext{PT}$-symmetry breaking in a Floquet system, revealing different growth regimes and their scaling laws.

Contribution

It provides a combined numerical and analytical analysis of OTOC dynamics at the $ ext{PT}$ transition in a non-Hermitian Floquet model, highlighting new scaling behaviors.

Findings

OTOCs saturate in the unbroken $ ext{PT}$ phase

Power-law growth of OTOCs near the transition with exponents > 2

Quadratic growth of OTOCs far beyond the transition

Abstract

We investigate both numerically and analytically the dynamics of out-of-time-order correlators (OTOCs) in a non-Hermitian kicked rotor model, addressing the scaling laws of the time dependence of OTOCs at the transition to the spontaneous $\mathcal{PT}$ symmetry breaking. In the unbroken phase of $\mathcal{PT}$ symmetry, the OTOCs increase monotonically and eventually saturate with time, demonstrating the freezing of information scrambling. Just beyond the phase transition points, the OTOCs increase in the power-laws of time, with the exponent larger than two. Interestingly, the quadratic growth of OTOCs with time emerges when the system is far beyond the phase transition points. Above numerical findings have been validated by our theoretical analysis, which provides a general framework with important implications for Floquet engineering and the information scrambling in chaotic systems.