# Reversible quantum information spreading in many-body systems near criticality

## TL;DR

This paper reveals that near criticality, many-body quantum systems exhibit a complex interplay of fast information scrambling and oscillatory localization-delocalization dynamics, with a unique timescale governing reversibility.

## Contribution

It demonstrates that quantum critical systems show reversible information dynamics with a characteristic timescale proportional to log N, combining semiclassical analysis and simulations.

## Key findings

- Fast initial scrambling near criticality
- Oscillatory localization and delocalization of information
- Recurrent behavior indicating reversibility

## Abstract

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. Most notably, it predicts an asymptotically constant local level spacing $\hbar/\tau$, again given by $\tau\! \sim\! \log N$. This unique timescale governs the long-time behavior of out-of-time-order correlators that feature quasi-periodic recurrences indicating reversibility.