Scaling laws of out-of-time-order correlators in a non-Hermitian kicked rotor model

Abstract

We investigate the dynamics of the out-of-time-order correlators (OTOCs) via a non-Hermitian extension of the quantum kicked rotor model, where the kicking potential satisfies PT-symmetry. The spontaneous PT-symmetry breaking emerges when the strength of the imaginary part of the kicking potential exceeds a threshold value. We find, both analytically and numerically, that in the broken phase of PT symmetry, the OTOCs rapidly saturate with time evolution. Interestingly, the late-time saturation value scales as a pow-law in the system size. The mechanism of such scaling law results from the interplay between the effects of the nonlocal operator in OTOCs and the time reversal induced by non-Hermitian-driven potential.

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

“…The dynamics of OTOCs, originally introduced by Lakin et al, in the study of quasiclassical theory of superconductivity [46], has received extensive studies in the fields of high energy physics [47][48][49], condensed matter physics [50][51][52][53][54][55] and quantum information [56][57][58]. It has been found that OTOCs can effectively detect quantum chaos [59][60][61][62], quantum thermalization [63], and information scrambling [64][65][66][67][68][69]. In the semiclassical limit, the exponential growth of OTOCs is governed by the Lyapunov exponent of classical chaos, which demonstrates a route of quantum-classical correspondence [70].…”