AUTHOR=Zhao Wen-Lei , Wang Ru-Ru 

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

JOURNAL=Frontiers in Physics

VOLUME=Volume 11 - 2023

YEAR=2023

URL=https://www.frontiersin.org/journals/physics/articles/10.3389/fphy.2023.1130225

DOI=10.3389/fphy.2023.1130225

ISSN=2296-424X

ABSTRACT=We investigate the dynamics of the out-of-time-ordered 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 nonlocal operator in OTOCs and the time reversal induced by non-Hermitian driven potential.