Fidelity Out-of-Time-Order Correlator in the Spin-Boson Model

In this article, using the numerically exact time-evolving matrix product operators method, we study the fidelity out-of-time-order correlator (FOTOC) in the unbiased spin-boson model at zero temperature. It is found that after the initial exponential growth of FOTOC, the information of the system dynamics will adulterate into the FOTOC. This makes the FOTOC an advanced epitome of the system dynamics, i.e., the FOTOC shows similar behavior to that of system dynamics within a shorter time interval. Eventually the progress of the FOTOC is ahead of the system dynamics, which can provide a prediction of the system dynamics.