Reversible quantum information spreading in many-body systems near criticality

Understand

Quantum chaotic interacting $N$-particle systems are assumed to show fast and irreversible spreading of quantum information on short (Ehrenfest) time scales $\sim\!\log N$.

• Here we show that, near criticality, certain many-body systems exhibit fast initial scrambling, followed subsequently by oscillatory behavior between reentrant localization and delocalization of information in Hilbert space.
• We consider both integrable and nonintegrable quantum critical bosonic systems with attractive contact interaction that exhibit locally unstable dynamics in the corresponding many-body phase space of the large-$N$ limit.
• Semiclassical quantization of the latter accounts for many-body correlations in excellent agreement with simulations.