# Are many-body localized systems stable in the presence of a small bath?

## TL;DR

This paper investigates the stability of many-body localization in large disordered quantum systems, finding that localization may be more robust than previously thought despite the presence of ergodic regions.

## Contribution

The study introduces a numerical approach to assess many-body localization stability in the thermodynamic limit considering low-disorder regions.

## Key findings

- Many-body localization appears more stable than recent theories suggest.
- Low-disorder regions do not necessarily lead to delocalization in large systems.
- Numerical results support the persistence of localization despite ergodic grains.

## Abstract

When pushed out of equilibrium, generic interacting quantum systems equilibrate locally and are expected to evolve towards a locally thermal description despite their unitary time evolution. Systems in which disorder competes with interactions and transport can violate this expectation by exhibiting many-body localization. The strength of the disorder with respect to the other two parameters drives a transition from a thermalizing system towards a non-thermalizing one. The existence of this transition is well established both in experimental and numerical studies for finite systems. However, the stability of many-body localization in the thermodynamic limit is largely unclear. With increasing system size, a generic disordered system will contain with high probability areas of low disorder variation. If large and frequent enough, those areas constitute ergodic grains which can hybridize and thus compete with localization. While the details of this process are not yet settled, it is conceivable that if such regions appear sufficiently often, they might be powerful enough to restore thermalization. We set out to shed light on this problem by constructing potential landscapes with low disorder regions and numerically investigating their localization behavior in the Heisenberg model. Our findings suggest that many-body localization may be much more stable than anticipated in other recent theoretical works.