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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. B89,144201 (2014)]: Localization protects quantum order of groundstate even inhigh excited eigenstates. In this work, we numerically investigate thelocalization protection for symmetry-protected-topological (SPT) order byconsidering a modified XXZ spin model, related to an interactingSu-Schrieffer-Heeger (SSH) model. We systematically study howMany-body-localization (MBL) protects SPT for different disorder types anddifferent forms of interactions. A certain disorder leads the clear degeneracyof the low-lying entanglement spectrum of each excited many-body eigenstates.This fact indicates that existence of edge modes, which is a hallmark of theSPT order, is protected by the MBL in excited many-body eigenstates. Inaddition, we also report how the MBL protected edge modes in excited many-bodyeigenstates fade away for a diagonal type disorder.

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