Linear and logarithmic entanglement production in an interacting chaotic quantum system

An isolated interacting quantum system whose internal dynamics make one subsystem act as an environment to the other is of great interest concerning entanglement spreading and decoherence. We investigate the entanglement dynamics of a pair of classically chaotic coupled kicked rotors. In this interacting system, one rotor acts as an environment to the other. As a consequence, it destroys the localization phenomenon, generally displayed by a single kicked rotor, and shows normal diffusion at long times. However, for weak coupling, the normal diffusion is preceded by an intermediate dynamical localization. We show that the localization-delocalization phenomenon directly corresponds to the system's distinct growth phases of the entanglement entropy. Surprisingly, the entanglement, characterized by the von Neumann entropy, shows a linear growth in the localized phase, followed by a logarithmic growth in the delocalized phase. We further provide an analytical expression for the time at which the entanglement entropy changes its profile from linear to logarithmic.