Stability and instability towards delocalization in MBL systems

TL;DR

This paper develops a quantitative theory for the stability of many-body localized (MBL) systems against ergodic regions, predicting destabilization under certain conditions, with numerical evidence supporting the theory.

Contribution

It introduces a theory based on ETH and perturbation theory that describes MBL stability without relying on LIOMs, and predicts long-term destabilization in specific cases.

Findings

MBL phase is stable in 1D at strong disorder

Destabilization occurs if interactions decay slower than exponential in 1D

MBL destabilizes in higher dimensions (d>1) over long times

Abstract

We propose a theory that describes quantitatively the (in)stability of fully MBL systems due to ergodic, i.e. delocalized, grains, that can be for example due to disorder fluctuations. The theory is based on the ETH hypothesis and elementary notions of perturbation theory. The main idea is that we assume as much chaoticity as is consistent with conservation laws. The theory describes correctly -even without relying on the theory of local integrals of motion (LIOM)- the MBL phase in 1 dimension at strong disorder. It yields an explicit and quantitative picture of the spatial boundary between localized and ergodic systems. We provide numerical evidence for this picture. When the theory is taken to its extreme logical consequences, it predicts that the MBL phase is destabilised in the long time limit whenever 1) interactions decay slower than exponentially in $d=1$ and 2) always in $d>1$. Finer numerics is required to assess these predictions.