# Topologically induced prescrambling and dynamical detection of topological phase transitions at infinite temperature

## TL;DR

This paper demonstrates that infinite-temperature out-of-time-order correlators can directly detect zero-temperature topological phase transitions, revealing a topological origin of prescrambling linked to Majorana zero modes in 1D systems.

## Contribution

It uncovers a novel topological phenomenon where high-temperature correlators probe zero-temperature phases via Majorana zero modes, bridging information scrambling and topological order.

## Key findings

- OTOCs at infinite temperature detect topological phase transitions.
- Majorana zero modes influence scrambling dynamics.
- Topological order induces prescrambling in nonintegrable models.

## Abstract

We report a numerical observation where the infinite-temperature out-of-time-order correlators (OTOCs) directly probe quantum phase transitions at zero temperature, in contrast to common intuition where low energy quantum effects are washed away by strong thermal fluctuations at high temperature. By comparing numerical simulations with exact analytic results, we determine that this phenomenon has a topological origin and is highly generic, as long as the underlying system can be mapped to a 1D Majorana chain. Using the Majorana basis, we show that the infinite-temperature OTOCs probe zero-temperature quantum phases via detecting the presence of Majorana zero modes at the ends of the chain that is associated with 1D $Z_2$ topological order. Hence, we show that strong zero modes also affect OTOCs and scrambling dynamics. Our results demonstrate an intriguing interplay between information scrambling and topological order, which leads to a new phenomenon in the scrambling of generic nonintegrable models: topological order induced prescrambling, paralleling the notion of prethermalization of two-time correlators, that defines a time-scale for the restricted scrambling of topologically-protected quantum information.