A note on the quasiperiodic many-body localization transition in dimension $d>1$

TL;DR

This paper investigates the stability of many-body localization in higher-dimensional quasiperiodic systems, suggesting stability in 2D but potential instability for dimensions three and above, impacting understanding of thermalization.

Contribution

It provides a theoretical analysis of MBL stability in quasiperiodic systems beyond one dimension, highlighting conditions for stability and potential instability in higher dimensions.

Findings

MBL is stable in 2D quasiperiodic systems at strong modulation

Avalanche effects strongly influence the MBL transition scaling

MBL likely unstable for dimensions three and higher

Abstract

The nature of the many-body localization (MBL) transition and even the existence of the MBL phase in random many-body quantum systems have been actively debated in recent years. In spatial dimension $d>1$, there is some consensus that the MBL phase is unstable to rare thermal inclusions that can lead to an avalanche that thermalizes the whole system. In this note, we explore the possibility of MBL in quasiperiodic systems in dimension $d>1$. We argue that (i) the MBL phase is stable at strong enough quasiperiodic modulations for $d = 2$, and (ii) the possibility of an avalanche strongly constrains the finite-size scaling behavior of the MBL transition. We present a suggestive construction that MBL is unstable for $d \geq 3$.