# Many-Body-Localization : Strong Disorder perturbative approach for the Local Integrals of Motion

## TL;DR

This paper revisits the strong disorder perturbative expansion of Local Integrals of Motion in random quantum spin models, linking it to dynamical memory, eigenstate properties, and analyzing the Many-Body Localization transition.

## Contribution

It introduces a perturbative approach to LIOMs that connects static and dynamic properties of the MBL phase, providing new insights into the transition.

## Key findings

- Perturbative expansion of LIOMs clarifies their role in MBL dynamics
- Links between LIOMs and local magnetization memory established
- Analysis of MBL transition via entanglement entropy in a toy model

## Abstract

For random quantum spin models, the strong disorder perturbative expansion of the Local Integrals of Motion (LIOMs) around the real-spin operators is revisited. The emphasis is on the links with other properties of the Many-Body-Localized phase, in particular the memory in the dynamics of the local magnetizations and the statistics of matrix elements of local operators in the eigenstate basis. Finally, this approach is applied to analyze the Many-Body-Localization transition in a toy model studied previously from the point of view of the entanglement entropy.