Characterization of quantum many-body chaos with quantum Lyapunov exponents and by two-point correlations: application to a generalized Sachdev-Ye-Kitaev model

We propose two quantities for characterization of quantum many-body chaos. Firstly, we define a simple quantum generalization of the spectrum of finite-time classical Lyapunov exponents. [1] We study its statistical features for the SYK model and find random matrix behavior, which is lost when the model is deformed away from chaos towards integrability [2] by a random two-fermion term. Secondly, we propose that two-point correlation functions can also characterize quantum many-body chaos, with numerical evidences for the SYK model as well as for the XXZ spin chain with random field, and discuss the plausibility of laboratory experiments.
[1] H. Gharibyan et al., arXiv:1809.01671.
[2] A. M. Garcia-Garcia et al., Phys. Rev. Lett. 120, 241603 (2018).