Similar Early Growth of Out-of-time-ordered Correlators in Quantum Chaotic and Integrable Ising Chains *

Hua Yan,Jiao-Zi Wang,Wen-Ge Wang

Fig. 1 (Color online) (a) The nearest-level-spacing distribution $P(s)$ (histogram) of the defect Ising chain under the periodic boundary condition. The dashed line (red) indicates the Wigner-Dyson distribution and the dashed-dotted line (blue) represents the Poisson distribution. (b) Similar to (a), but under the open boundary condition. (c) The distribution of rescaled components $R_{\alpha i}$ of eigenfunctions in the middle energy region (squares). The dashed line (red) indicates the Gaussian distribution. Parameters: $d_1=0.5$, $d_k=1.0$, $k=6$, and $L=11$ (the same for the following figures).