Chain breaking and Kosterlitz-Thouless scaling at the many-body localization transition in the random-field Heisenberg spin chain

Nicolas Laflorencie,Gabriel Lemarié,Nicolas Macé

doi:10.1103/physrevresearch.2.042033

Abstract

Despite tremendous theoretical efforts to understand subtleties of the many-body localization (MBL) transition, many questions remain open, in particular concerning its critical properties. Here we make the key observation that MBL in one dimension is accompanied by a spin freezing mechanism which causes chain breakings in the thermodynamic limit. Using analytical and numerical approaches, we show that such chain breakings directly probe the typical localization length, and that their scaling properties at the MBL transition agree with the Kosterlitz-Thouless scenario predicted by phenomenological renormalization group approaches.

Highlights

The field of interacting quantum systems in the presence of disorder has attracted a lot of attention over the past two decades
Using analytical and numerical approaches, we show that such chain breaks directly probe the typical localization length and that their scaling properties at the many-body localization (MBL) transition agree with the Kosterlitz-Thouless scenario predicted by phenomenological renormalization group approaches
Our key result is that the extreme value statistics in the MBL regime gives a direct access to the typical localization length ζ and the typical l-bit extension of the MBL states

Summary

Rapid Communications

Nicolas Laflorencie,1,* Gabriel Lemarié ,1,2,3,† and Nicolas Macé 1,‡ 1Laboratoire de Physique Théorique, IRSAMC, Université de Toulouse, CNRS, UPS, France. Despite tremendous theoretical efforts to understand subtleties of the many-body localization (MBL) transition, many questions remain open, in particular concerning its critical properties. We make the key observation that MBL in one dimension is accompanied by a spin freezing mechanism which causes chain breaks in the thermodynamic limit. Using analytical and numerical approaches, we show that such chain breaks directly probe the typical localization length and that their scaling properties at the MBL transition agree with the Kosterlitz-Thouless scenario predicted by phenomenological renormalization group approaches

Introduction

Published by the American Physical Society