# Delocalized Glassy Dynamics and Many Body Localization

## TL;DR

This paper investigates slow, glassy-like dynamics near the many-body localization transition using a Bethe lattice model, revealing power-law behaviors and discussing the nature of the intermediate phase.

## Contribution

It introduces a Bethe lattice toy model to analyze slow dynamics and spectral statistics related to many-body localization, providing new insights into the transition.

## Key findings

- Observation of slow dynamics and power-laws similar to experiments
- Relation of non-ergodic spectral statistics to slow behavior
- Discussion of finite-size effects and transition scenarios

## Abstract

We analyze the unusual slow dynamics that emerges in the bad metal delocalized phase preceding the Many-Body Localization transition by using single-particle Anderson Localization on the Bethe lattice as a toy model of many-body dynamics in Fock space. We probe the dynamical evolution by measuring observables such as the imbalance and equilibrium correlation functions, which display slow dynamics and power-laws strikingly similar to the ones observed in recent simulations and experiments. We relate this unusual behavior to the non-ergodic spectral statistics found on Bethe lattices. We discuss different scenarii, such as a true intermediate phase which persists in the thermodynamic limit versus a glassy regime established on finite but very large time and length-scales only, and their implications for real space dynamical properties. In the latter, slow dynamics and power-laws extend on a very large time-window but are eventually cut-off on a time-scale that diverges at the MBL transition.