Many-body localization, symmetry, and topology

TL;DR

This paper reviews how many-body localization can preserve topological quantum order in isolated systems out of equilibrium, emphasizing the roles of symmetry and dimensionality in stabilizing topological phases.

Contribution

It provides a comprehensive overview of recent progress in understanding the interplay between many-body localization, symmetry, and topology in quantum systems.

Findings

Many-body localization prevents thermalization, preserving quantum order.

Localization can protect topological phases out of equilibrium.

Symmetry and dimensionality influence the stability of localized topological states.

Abstract

We review recent developments in the study of out-of-equilibrium topological states of matter in isolated systems. The phenomenon of many-body localization, exhibited by some isolated systems usually in the presence of quenched disorder, prevents systems from equilibrating to a thermal state where the delicate quantum correlations necessary for topological order are often washed out. Instead, many-body localized systems can exhibit a type of eigenstate phase structure wherein their entire many-body spectrum is characterized by various types of quantum order, usually restricted to quantum ground states. After introducing many-body localization and explaining how it can protect quantum order, we then explore how the interplay of symmetry and dimensionality with many-body localization constrains its role in stabilizing topological phases out of equilibrium.