Topological Anderson insulators represent a class of disorder-induced, nontrivial topological states of matter. In this study, we propose a feasible strategy to unveil and design topological Anderson insulators protected by latent symmetries. These are not visible in the original system, but become obvious after performing an isospectral reduction. Using this technique, we design a family of disordered multiatomic chains that exhibit latent chiral symmetry or mirror (inversion) symmetry. Using topological invariants, bulk polarization, and the divergence of localization length of the topological bound edge states in the reduced disordered system, we show how to identify the gapped and ungapped topological Anderson states in the original systems. Our work thus extends the concept of topological Anderson insulating phases protected by geometric symmetries and tenfold-way classification to the various types of latent symmetry cases. Overall, our work paves the way for exploiting topological Anderson insulators in terms of latent symmetries.

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• Anderson localization
• Symmetry protected topological states
• Disordered systems
• Tight-binding model