Scenario for delocalization in translation invariant systems

TL;DR

This paper explores the potential for many-body localization in translation-invariant systems, highlighting how mobile resonant spots may lead to delocalization over long timescales, contrasting with disordered systems.

Contribution

It introduces a novel analysis of delocalization mechanisms in translation-invariant systems, emphasizing the role of mobile resonant spots and providing both perturbative and non-perturbative arguments.

Findings

Resonant spots are rare and mobile in translation-invariant systems.

Mobile resonant spots can facilitate delocalization over long timescales.

Explicit perturbative and ergodicity-based non-perturbative arguments are provided.

Abstract

We investigate the possibility of Many-Body Localization in translation invariant Hamiltonian systems, which was recently brought up by several authors. A key feature of Many-Body Localized disordered systems is recovered, namely the fact that resonant spots are rare and far-between. However, we point out that resonant spots are mobile, unlike in models with strong quenched disorder, and that these mobile spots constitute a possible mechanism for delocalization, albeit possibly only on very long timescales. In some models, this argument for delocalization can be made very explicit in first order of perturbation theory in the hopping. For models where this does not work, we present instead a non-perturbative argument that relies solely on ergodicity inside the resonant spots.