# Detection of quantum phases via out-of-time-order correlators

## TL;DR

This paper explores how out-of-time-order correlators (OTOCs) can be used to detect quantum phase transitions, providing an analytical framework and numerical validation with the XXZ model.

## Contribution

It introduces a new analytical method linking OTOC dynamics to quantum phases, applicable to various quantum phase transitions.

## Key findings

- OTOCs can dynamically indicate quantum phases.
- Analytical relations between OTOCs and phase transitions are established.
- Numerical confirmation with the XXZ model supports the theory.

## Abstract

We elucidate the relation between out-of-time-order correlators (OTOCs) and quantum phase transitions via analytically studying the OTOC dynamics in a degenerate spectrum. Our method points to key ingredients to dynamically detect quantum phases via out-of-time-order correlators for a wide range of quantum phase transitions and explains the existing numerical results in the literature. We apply our method to a critical model, XXZ model that numerically confirms our predictions.