# Logarithmic spreading of out-of-time-ordered correlators without many-body localization

## TL;DR

This paper investigates the behavior of out-of-time-ordered correlators in a disorder-free localized model, revealing a surprising logarithmic spreading of correlations typically associated with many-body localization, even in non-interacting systems.

## Contribution

The study demonstrates logarithmic correlation spreading in a disorder-free, non-interacting model, challenging the conventional association with many-body localization.

## Key findings

- Logarithmic spreading of OTOCs observed in the model.
- Proposed a novel Loschmidt echo protocol to probe correlation spreading.
- Logarithmic spreading is a generic feature of localized systems, regardless of interactions.

## Abstract

Out-of-time-ordered correlators (OTOCs) describe information scrambling under unitary time evolution, and provide a useful probe of the emergence of quantum chaos. Here we calculate OTOCs for a model of disorder-free localization whose exact solubility allows us to study long-time behaviour in large systems. Remarkably, we observe logarithmic spreading of correlations, qualitatively different to both thermalizing and Anderson localized systems. Rather, such behaviour is normally taken as a signature of many-body localization, so that our findings for an essentially non-interacting model are surprising. We provide an explanation for this unusual behaviour, and suggest a novel Loschmidt echo protocol as a probe of correlation spreading. We show that the logarithmic spreading of correlations probed by this protocol is a generic feature of localized systems, with or without interactions.