Out-of-time-order correlations in the quasiperiodic Aubry-André model

We study out-of-time-ordered correlators (OTOC) in a free fermionic model with a quasiperiodic potential. This model is equivalent to the Aubry-André model and features a phase transition from an extended phase to a localized phase at a nonzero value of the strength of the quasiperiodic potential. We investigate five different time regimes of interest for out-of-time-ordered correlators: early, wave front, x=vBt, late time equilibration, and infinite time. For the early time regime we observe a power law for all potential strengths. For the precursor time regime preceding the wave front we confirm a recently proposed universal form and use it to extract the characteristic velocity of the wave front for the present model. A Gaussian waveform is observed to work well in the time regime surrounding x=vBt, the wave front arrival time. Our main result is for the late time equilibration regime where we derive a finite time equilibration bound for the OTOC, bounding the correlator's distance from its late time value. The bound impose strict limits on equilibration of the OTOC in the extended regime and is valid not only for the Aubry-André model but for any quadratic model. Finally, momentum out-of-time-ordered correlators for the Aubry-André model are studied where large values of the OTOC are observed at late times at the critical point.