Nonlinear dynamics and quantum chaos of a family of kicked $p$-spin models

TL;DR

This paper introduces a family of kicked p-spin models generalizing the quantum kicked top, analyzing their classical nonlinear dynamics, chaos transition, and quantum chaos signatures, including out-of-time-order correlator growth.

Contribution

It provides a comprehensive classical and quantum analysis of the nonlinear dynamics and chaos in generalized kicked p-spin models, extending understanding beyond the well-studied p=2 case.

Findings

Classical chaos transition characterized for different p values.

Quantum chaos signatures linked to classical Lyapunov exponents.

Classification scheme distinguishing models based on p parity and value.

Abstract

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, Ku\'s, 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.