# Many-body-localization induced protection of symmetry-protected topological order in a XXZ spin model

## TL;DR

This paper demonstrates through numerical simulations that many-body localization can protect symmetry-protected topological order in excited states of a modified XXZ spin model, highlighting the role of disorder type in preserving edge modes.

## Contribution

It provides the first detailed numerical analysis of how MBL protects SPT order in excited states within a XXZ spin model related to the SSH model, considering different disorder types.

## Key findings

- MBL preserves edge modes in excited states with certain disorder.
- Degeneracy in entanglement spectrum indicates protected SPT order.
- Diagonal disorder leads to the loss of MBL-protected edge modes.

## Abstract

There is a counter-intuitive expectation proposed by Huse {\it et al} [Phys. Rev. B {\bf 88}, 014206 (2013)], and Chandran {\it et al} [Phys. Rev. B 89,144201 (2014)]: Localization protects quantum order of groundstate even in high excited eigenstates. In this work, we numerically investigate the localization protection for symmetry-protected-topological (SPT) order by considering a modified XXZ spin model, related to an interacting Su-Schrieffer-Heeger (SSH) model. We systematically study how Many-body-localization (MBL) protects SPT for different disorder types and different forms of interactions. A certain disorder leads the clear degeneracy of the low-lying entanglement spectrum of each excited many-body eigenstates. This fact indicates that existence of edge modes, which is a hallmark of the SPT order, is protected by the MBL in excited many-body eigenstates. In addition, we also report how the MBL protected edge modes in excited many-body eigenstates fade away for a diagonal type disorder.