Maximum velocity quantum circuits

We consider the long-time limit of out-of-time-order correlators (OTOCs) in two classes of quantum lattice models with time evolution governed by local unitary quantum circuits and maximal butterfly velocity upsilon(B) = 1. Using a transfer matrix approach, we present analytic results for the long-time value of the OTOC on and inside the light cone. First, we consider dual-unitary circuits with various levels of ergodicity, including the integrable and nonintegrable kicked Ising model, where we show exponential decay away from the light cone and relate both the decay rate and the long-time value to those of the correlation functions. Second, we consider a class of kicked XY models similar to the integrable kicked Ising model, again satisfying upsilon(B) = 1, highlighting that maximal butterfly velocity is not exclusive to dual-unitary circuits.