# Dynamical Scaling Laws of Out-of-Time-Ordered Correlators

## TL;DR

This paper demonstrates that out-of-time-ordered correlators (OTOCs) in quantum many-body systems near critical points follow universal dynamical scaling laws, enabling the identification of quantum critical points and extraction of critical exponents.

## Contribution

It introduces the concept that OTOCs obey universal scaling laws near quantum critical points, linking chaos and critical phenomena in quantum systems.

## Key findings

- OTOCs follow universal dynamical scaling laws near critical points
- The butterfly velocity exhibits universality in chaotic models
- Critical properties can be extracted from OTOC measurements

## Abstract

The out-of-time-ordered correlator (OTOC) is central to the understanding of information scrambling in quantum many-body systems. In this work, we show that the OTOC in a quantum many-body system close to its critical point obeys dynamical scaling laws which are specified by a few universal critical exponents of the quantum critical point. Such scaling laws of the OTOC imply a universal form for the butterfly velocity of a chaotic system in the quantum critical region and allow one to locate the quantum critical point and extract all universal critical exponents of the quantum phase transitions. We numerically confirm the universality of the butterfly velocity in a chaotic model, namely the transverse axial next-nearest-neighbor Ising model, and show the feasibility of extracting the critical properties of quantum phase transitions from OTOC using the Lipkin-Meshkov-Glick (LMG) model.