We introduce kicked $p$-spin models describing a family of transverse Ising-like models for an ensemble of spin-$1/2$ particles with all-to-all $p$-body interaction terms occurring periodically in time as delta-kicks. This is the natural generalization of the well-studied quantum kicked top $(p=2)$ [Haake, Kuś, and Scharf, Z. Phys. B 65, 381 (1987)]. We fully characterize the classical nonlinear dynamics of these models, including the transition to global Hamiltonian chaos. The classical analysis allows us to build a classification for this family of models, distinguishing between $p=2$ and $p>2$, and between models with odd and even $p$'s. Quantum chaos in these models is characterized in both kinematic and dynamic signatures. For the latter, we show numerically that the growth rate of the out-of-time-order correlator is dictated by the classical Lyapunov exponent. Finally, we argue that the classification of these models constructed in the classical system applies to the quantum system as well.

• Received 2 March 2021
• Accepted 27 April 2021

DOI:https://doi.org/10.1103/PhysRevE.103.052212