Research On The Diagnosis Of Quantum Chaos In Multipartite Systems

Quantum chaos is a ubiquitous phenomenon in condensed matter physics,quantum information,and high-energy physics.Quantum chaotic diagnostics,such as spectral form factor,out-of-time-order correlator,Loschmidt echo,are focused on probing the global chaos of a single system or a multipartite system.Such methods have great limitations when we are intending to detect the local chaotic features of each subsystem in a multipartite system.In order to capture the local and global chaos of multipartite quantum systems,a new approach is proposed by introducing the characteristic functions of different energy observables,which can be the Hamiltonian of a subsystem or the interaction energy.The characteristic function is the Fourier transform of the energy spectral distribution,including the correlation among all energy levels.Similar to the spectral form factor,the span of the correlation hole in a logarithmic figure of the characteristic function conveys the strength of the chaos.In addition,the characteristic function can be experimentally demonstrated by using single-qubit interferometry with an ancillary qubit.For illustration,we consider the coupled Gaussian orthogonal ensemble model as an example.We find that the interactions among subsystems will dominate when the couplings are enhanced.Since the Hamiltonian of the interaction is selected as the direct product of Gaussian orthogonal ensembles,the statistics of its eigenvalues will break the Wigner-Dyson distribution,and the associated correlation hole of the characteristic function will gradually vanish,resulting in the global chaotic feature gradually weakened.In addition,we numerically observe that the characteristic function of the global system can be constructed by the local characteristic functions of the subsystem.The more complex the couplings,the greater its influence on the global chaotic features of the system.The above phenomena are further verified in other models,such as the coupled Sachdev-Ye-Kitaev model and the coupled spin model.Using characteristic function to diagnose the local and global chaotic features of multipartite quantum systems will help us deepen our understanding of complex quantum systems,and will also provide a theoretical basis for the interplay of quantum chaos,quantum information,and holographic duality.