  We study non-equilibrium dynamics induced by a sudden quench of strongly
correlated Hamiltonians with all-to-all interactions. By relying on a
Sachdev-Ye-Kitaev (SYK) based quench protocol, we show that the time evolution
of simple spin-spin correlation functions is highly sensitive to the degree of
locality of the corresponding operators, once an appropriate set of fundamental
fields is identified. By tracking the time-evolution of specific spin-spin
correlation functions and their decay, we argue that it is possible to
distinguish between operator hopping and operator growth dynamics; the latter
being a hallmark of quantum chaos in many-body quantum systems. Such
observation, in turn, could constitute a promising tool to probe the emergence
of chaotic behavior, rather accessible in state-of-the-art quench setups.
