# Renormalization-group study of the many-body localization transition in one dimension

## TL;DR

This paper develops a new strong-randomness renormalization group method to study the many-body localization transition in one-dimensional quantum systems, revealing a Kosterlitz-Thouless-like flow and fractal thermal inclusions.

## Contribution

It introduces a novel RG approach that characterizes insulating blocks with two lengths, providing new insights into the MBL phase and transition without intermediate critical phases.

## Key findings

- MBL phase governed by a RG fixed line with a decay length parameter
- Thermal inclusions within MBL phase have fractal geometry
- Transition exhibits Kosterlitz-Thouless-like RG flow

## Abstract

Using a new approximate strong-randomness renormalization group (RG), we study the many-body localized (MBL) phase and phase transition in one-dimensional quantum systems with short-range interactions and quenched disorder. Our RG is built on those of Zhang $\textit{et al.}$ [1] and Goremykina $\textit{et al.}$ [2], which are based on thermal and insulating blocks. Our main addition is to characterize each insulating block with two lengths: a physical length, and an internal decay length $\zeta$ for its effective interactions. In this approach, the MBL phase is governed by a RG fixed line that is parametrized by a global decay length $\tilde{\zeta}$, and the rare large thermal inclusions within the MBL phase have a fractal geometry. As the phase transition is approached from within the MBL phase, $\tilde{\zeta}$ approaches the finite critical value corresponding to the avalanche instability, and the fractal dimension of large thermal inclusions approaches zero. Our analysis is consistent with a Kosterlitz-Thouless-like RG flow, with no intermediate critical MBL phase.