Correlation Between Information Scrambling And Quantum Chaos In Non-Hermitian Floquet Systems

In recent years,out-of-time ordered correlators(OTOCs)have attracted widespread attention in many fields such as high energy physics,condensed matter physics,and quantum information.Under the semiclassical limit,its exponential growth rate is similar to the Lyapunov exponent of classical chaos,which proves the quantum classical correspondence.Therefore,OTOCs is regarded as a new indicator for determining quantum chaos.From the perspective of quantum information,OTOCs reflect the propagation of quantum information in the entire system space,which is mainly quantified by the growth of local operators over evolution time.Nowadays,OTOCs are widely used to diagnose multi body localization,quantum entanglement,quantum heating,and multi body chaos,thereby promoting in-depth research in the field of multi body physics.The study of dynamics of periodically driven quantum systems is a hot topic in the fields of quantum chaos and quantum information,providing an ideal platform for studying fundamental problems in physics.Non Hermitian systems are extensions of Hermitian systems.Many systems,such as optical propagation in "gain or loss" media,electron transmission in dissipative circuits,and cold atoms in special magneto-optical traps,are described using non Hermitian theory.Currently,in the field of quantum chaos,finding the growth mode of operators is still a long-standing problem.Based on this,this paper studies the dynamic scaling laws of two different structures of non sequential correlators from both theoretical analysis and numerical simulation on the basis of non Hermitian periodic drive systems.The main work includes the following two aspects:1.The first type of OTOCs is constructed by the angular coordinate operator θ and the m-power of angular momentum operator p.It is found that during the parity-time(PT)symmetry breaking phase,OTOCs quickly saturate over time,and the saturation value is a power law function of the system dimension,which is evidence of the scaling of OTOCs with the size of the system.The generation principle of this mechanism is revealed through numerical research.One is that the effect of nonlocal operators θ constructing OTOCs act on quantum states,resulting in power law attenuation of wave functions in momentum space,and the shape of the wave functions remains unchanged during time inversion;The other is that the non Hermitian Kick potential induces nearly perfect time inversion of quantum states in momentum space.Based on the power law attenuation of the wave function,the late saturation values of the three components of OTOCs were analytically derived,and our numerical results were in perfect agreement with the analytical predictions.This discovery deepens the understanding of quantum information perturbation in non Hermitian chaotic systems.2.The second type of OTOCs are constructed by two angular momentum operators.We mainly study the dynamic scaling laws of OTOCs in PTKR models at different stages of PT symmetry from theoretical analysis and numerical calculations.It is found that during the unbroken phase of PT symmetry,OTOCs monotonically increase over time and eventually tend to saturate,that is because the dynamic localization of energy diffusion inhibiting the growth of OTOCs.Through numerical research,it is proved that the saturation value of OTOCs is a power law function of the real part of the kick potential energy.In the PT symmetry breaking stage,it is found that the growth rate of OTOCs is a power law function of time.When the system just exceeds the phase transition point,its power exponent is greater than 2,while for systems far beyond the phase transition point,its power exponent is equal to2.Through a detailed analysis of wave packet dynamics during time inversion,the mechanism of dynamic localization and power law increase in OTOCs is revealed.Studies have shown that the dynamics of OTOCs can be used to diagnose spontaneous PT symmetry breaking.