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

Fausto Borgonovi, Felix M. Izrailev, Lea F. Santos

Published 2023-07-11Version 1

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