# Many body localization with long range interactions

## TL;DR

This paper presents non-perturbative theoretical arguments suggesting that many body localization (MBL) can occur in systems with long-range interactions, challenging the conventional belief that MBL only exists in short-range systems.

## Contribution

It introduces non-perturbative arguments demonstrating the possibility of MBL in long-range interacting systems across different dimensions, extending the understanding of MBL physics.

## Key findings

- MBL can arise in 1D systems with ~ r interactions.
- MBL can occur in 2D systems with log r interactions.
- Potential extension of MBL to 3D systems with 1/r interactions.

## Abstract

Many body localization (MBL) has emerged as a powerful paradigm for understanding non-equilibrium quantum dynamics. Folklore based on perturbative arguments holds that MBL only arises in systems with short range interactions. Here we advance non-perturbative arguments indicating that MBL can arise in systems with long range (Coulomb) interactions. In particular, we show using bosonization that MBL can arise in one dimensional systems with ~ r interactions, a problem that exhibits charge confinement. We also argue that (through the Anderson-Higgs mechanism) MBL can arise in two dimensional systems with log r interactions, and speculate that our arguments may even extend to three dimensional systems with 1/r interactions. Our arguments are `asymptotic' (i.e. valid up to rare region corrections), yet they open the door to investigation of MBL physics in a wide array of long range interacting systems where such physics was previously believed not to arise.