# Butterfly effect in interacting Aubry-Andre model: thermalization, slow scrambling, and many-body localization

## TL;DR

This paper investigates the intermediate dynamical phase in the interacting Aubry-Andre model, revealing a regime with zero butterfly velocity and power-law information spreading, which may explain slow dynamics observed experimentally.

## Contribution

It introduces a novel dynamical measure to identify an intermediate phase with slow information spreading and analyzes its entanglement properties, challenging the eigenstate thermalization hypothesis.

## Key findings

- Identification of an intermediate phase with zero butterfly velocity.
- Power-law spreading of information in the intermediate phase.
- Strong entanglement fluctuations inconsistent with thermalization.

## Abstract

The many-body localization transition in quasiperiodic systems has been extensively studied in recent ultracold atom experiments. At intermediate quasiperiodic potential strength, a surprising Griffiths-like regime with slow dynamics appears in the absence of random disorder and mobility edges. In this work, we study the interacting Aubry-Andre model, a prototype quasiperiodic system, as a function of incommensurate potential strength using a novel dynamical measure, information scrambling, in a large system of 200 lattice sites. Between the thermal phase and the many-body localized phase, we find an intermediate dynamical phase where the butterfly velocity is zero and information spreads in space as a power-law in time. This is in contrast to the ballistic spreading in the thermal phase and logarithmic spreading in the localized phase. We further investigate the entanglement structure of the many-body eigenstates in the intermediate phase and find strong fluctuations in eigenstate entanglement entropy within a given energy window, which is inconsistent with the eigenstate thermalization hypothesis. Machine-learning on the entanglement spectrum also reaches the same conclusion. Our large-scale simulations suggest that the intermediate phase with vanishing butterfly velocity could be responsible for the slow dynamics seen in recent experiments.