# Gauging classical and quantum integrability through out-of-time ordered correlators

## TL;DR

This paper investigates the long-time behavior of out-of-time-order correlators (OTOCs) in quantum systems to effectively distinguish between integrable and chaotic regimes, providing a new diagnostic tool for quantum chaos.

## Contribution

It introduces a novel approach to gauge quantum chaos through long-time OTOC analysis across different quantum systems, including maps and spin chains.

## Key findings

- OTOCs can detect the transition from integrability to chaos.
- Long-time OTOC behavior correlates with spectral and eigenstate indicators.
- High accuracy in systems with classical analogues for identifying subtle transition features.

## Abstract

Out-of-time-order correlators (OTOCs) have been proposed as a probe of chaos in quantum mechanics, on the basis of their short-time exponential growth found in some particular set-ups. However, it has been seen that this behavior is not universal. Therefore, we query other quantum chaos manifestations arising from the OTOCs and we thus study their long-time behavior in systems of completely different nature: quantum maps, which are the simplest chaotic one-body system and spin chains, which are many-body systems without a classical limit. It is shown that studying the long-time regime of the OTOCs it is possible to detect and gauge the transition between integrability and chaos, and we benchmark the transition with other indicators of quantum chaos based on the spectra and the eigenstates of the systems considered. For systems with classical analogue, we show that the proposed OTOC indicators have a very high accuracy that allow to detect subtle features along the integrability-to-chaos transition.