# Instability of many-body localized systems as a phase transition in a nonstandard thermodynamic limit

## TL;DR

This paper investigates the nature of the many-body localization phase transition in higher dimensions, proposing a nonstandard thermodynamic limit to understand the avalanche instability and the onset of thermalization.

## Contribution

It introduces a novel scaling approach to define the MBL phase transition in higher dimensions, highlighting the role of avalanche instabilities and entanglement spreading.

## Key findings

- MBL transition in higher dimensions involves avalanche instabilities.
- Entanglement begins to spread at the transition point, leading to thermalization.
- One-dimensional MBL is a special case with a different transition mechanism.

## Abstract

The many-body localization (MBL) phase transition is not a conventional thermodynamic phase transition. Thus to define the phase transition one should allow the possibility of taking the limit of an infinite system in a way that is not the conventional thermodynamic limit. We explore this for the so-called "avalanche" instability due to rare thermalizing regions in the MBL phase for quenched-random systems in more than one spatial dimension, finding an unconventional way of scaling the systems so that they do have a type of phase transition. These arguments suggest that the MBL phase transition in systems with short-range interactions in more than one dimension is a transition where entanglement in the eigenstates begins to spread in to some typical regions: the transition is set by when the avalanches start. Once this entanglement gets started, the system does thermalize. From this point of view, the much-studied case of one-dimensional MBL with short-range interactions is a special case with a different, and in some ways more conventional, type of phase transition.