Ergodic inclusions in many body localized systems

TL;DR

This paper studies how ergodic inclusions affect many-body localized systems, suggesting that such inclusions can destabilize localization at intermediate disorder, but numerical evidence remains inconclusive.

Contribution

It provides numerical analysis of ergodic bubbles in many-body localized systems, exploring their destabilizing effects at intermediate disorder levels.

Findings

Ergodic bubbles can destabilize localization at certain disorder strengths.

Response to bubbles decays slowly or not at all with distance at intermediate disorder.

Numerical results are inconclusive regarding the thermodynamic limit.

Abstract

We investigate the effect of ergodic inclusions in putative many-body localized systems. To this end, we consider the random field Heisenberg chain, which is many-body localized at strong disorder and we couple it to an ergodic bubble, modeled by a random matrix Hamiltonian. Recent theoretical work suggests that the ergodic bubble destabilizes the apparent localized phase at intermediate disorder strength and finite sizes. We tentatively confirm this by numerically analyzing the response of the local thermality, quantified by one-site purities, to the insertion of the bubble. For a range of intermediate disorder strengths, this response decays very slowly, or not at all, with increasing distance to the bubble. This suggests that at those disorder strengths, the system is delocalized in the thermodynamic limit. However, the numerics is unfortunately not unambiguous and we cannot definitely rule out artefacts.