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

Abstract

There is a counterintuitive expectation proposed by Huse et al. [Phys. Rev. B 88, 014206 (2013)PRBMDO1098-012110.1103/PhysRevB.88.014206] and Chandran et al. [Phys. Rev. B 89, 144201 (2014)PRBMDO1098-012110.1103/PhysRevB.89.144201]: Localization protects the quantum order of the ground state, even in highly excited eigenstates. In this Rapid Communication, 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 to the clear degeneracy of the low-lying entanglement spectrum of each excited many-body eigenstate. This fact indicates that the existence of edge modes, which is a hallmark of 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.