# Slow Dynamics in Translation-Invariant Quantum Lattice Models

## TL;DR

This paper investigates the potential for slow, localized-like dynamics in translation-invariant quantum lattice models, revealing regimes where systems exhibit slow delocalization despite lacking disorder, challenging traditional views on many-body localization.

## Contribution

The authors develop a degenerate perturbation theory approach to identify and estimate slow dynamical regimes and delocalization times in translation-invariant quantum systems, highlighting robustness of integrability.

## Key findings

- Identification of slow dynamical regimes in translation-invariant models
- Construction of models with transient localization-like behavior
- Estimation of delocalization time scales in these models

## Abstract

Many-body quantum systems typically display fast dynamics and ballistic spreading of information. Here we address the open problem of how slow the dynamics can be after a generic breaking of integrability by local interactions. We develop a method based on degenerate perturbation theory that reveals slow dynamical regimes and delocalization processes in general translation invariant models, along with accurate estimates of their delocalization time scales. Our results shed light on the fundamental questions of robustness of quantum integrable systems and the possibility of many-body localization without disorder. As an example, we construct a large class of one-dimensional lattice models where, despite the absence of asymptotic localization, the transient dynamics is exceptionally slow, i.e., the dynamics is indistinguishable from that of many-body localized systems for the system sizes and time scales accessible in experiment and numerical simulations.