# Exploring many-body localization in quantum systems coupled to an environment via Wegner-Wilson flows

## TL;DR

This paper investigates how many-body localization can occur in a clean quantum chain when coupled to a disordered environment, using flow equations to identify conditions and emergent conserved quantities.

## Contribution

It introduces a flow equation approach to analyze many-body localization proximity effects in coupled quantum chains, revealing the role of environment density and coupling geometry.

## Key findings

- Localization in the clean chain depends on environment density exceeding a threshold.
- Many-body localization is characterized by local integrals of motion.
- Emergent quasi-conserved charges influence intermediate-time dynamics.

## Abstract

Inspired by recent experiments on many-body localized systems coupled to an environment, we apply a Flow Equation method to study the problem of a disorder chain of spinless fermions, coupled via density-density interactions to a second clean chain of spinless fermions. In particular, we focus on the conditions for the onset of a many-body localized phase in the clean sector of our model by proximity to the dirty one. We find that a many-body localization proximity effect in the clean component is established when the density of dirty fermions exceeds a threshold value. From the flow equation method we find that, similar to many-body localization in a single chain, the many-body localization proximity effect is also described by an extensive set of local integrals of motion. Furthermore, by tuning the geometry of the inter-chain couplings, we show that the dynamics of the model is ruled, on intermediate time scales, by an emergent set of quasi-conserved charges.