We study information scrambling, as diagnosed by the out-of-time order correlations (OTOCs), in a system of large spins collectively interacting via spatially inhomogeneous and incommensurate exchange couplings. The model is realizable in a cavity QED system in the dispersive regime. Fast scrambling, signaled by an exponential growth of the OTOCs, is observed when the couplings do not factoriZe into the product of a pair of local interaction terms, and at the same time the state of the spins points initially coplanar to the equator of the Bloch sphere. When one of these conditions is not realized, OTOCs grow algebraically with an exponent sensitive to the orientation of the spins in the initial state. The impact of initial conditions on the scrambling dynamics is attributed to the presence of a global conserved quantity, which critically slows down the evolution for initial states close to the poles of the Bloch sphere.

• Received 1 October 2018
• Revised 28 November 2018

DOI:https://doi.org/10.1103/PhysRevA.99.051803