Many-body localization and delocalization from the perspective of Integrals of Motion

TL;DR

This paper investigates many-body localization and delocalization by analyzing integrals of motion (IOMs), revealing that localized IOMs are typical across disorder strengths and highlighting the role of rare fluctuations in the transition.

Contribution

The study introduces a method using displacement transformations to analyze IOMs, providing new insights into their localization properties across the MBL transition.

Findings

Typical IOMs are localized at all disorder levels.

Rare fluctuations play a crucial role in the delocalization transition.

Quantities can be computed via an operator expansion in IOMs.

Abstract

We study many-body localization (MBL) and delocalization from the perspective of integrals of motion (IOMs). MBL can be understood phenomenologically through the existence of macroscopically many localized IOMs. However, IOMs exist for all many-body systems, and non-localized IOMs determine properties on the ergodic side of the MBL transition too. Here we explore their properties using our method of displacement transformations. We show how different quantities can be calculated using the IOMs as an expansion in the number of operators. For all values of disorder the typical IOMs are localized, suggesting the importance of rare fluctuations in understanding the delocalization transition.