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We study quench dynamics in a one-dimensional interacting spin model that isstrongly chaotic in the classical and quantum domain. We use the knowledge ofthe quantum-classical correspondence developed in [Phys. Rev. B 107, 155143(2023)] to elucidate the mechanism of the system relaxation process. Itactually involves two mechanisms, one due to linear parametric instability andthe other caused by nonlinearity. We show that the relaxation of thenoninteracting energy (global quantity) and of the onsite magnetization (localobservable) is mainly due to the first mechanism, referred to as linear chaos.With a semi-analytical approach based on classical ergodicity, we find that therelaxation timescale of both quantities is independent of the system size forboth the classical and the quantum case. We also verify that the spread of thenoninteracting energy in the energy shell is diffusive-like. In contrast tothese results, the number of principal components, which quantifies how theinitial state spreads in the many-body Hilbert space and does not have aclassical counterpart, grows exponentially in time and has a relaxation timethat depends on the number of spins.

Quantum-Classical Correspondence for the Relaxation Dynamics of Many-Body Spin Systems: Linear Chaos and Diffusion in the Energy Shell