K
KITT
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Latent-Symmetry-Protected Topological Anderson Insulators via Isospectral Reduction
The paper's contribution: a route to topological Anderson insulating phases whose protecting symmetry is invisible in the lattice. Isospectral reduction from graph theory collapses a disordered multi-atomic chain onto an effective dimerised chain with energy-dependent onsite potentials and hoppings while preserving the spectrum and the projected eigenvectors, so a building block with no apparent structural symmetry can reduce to one that is chiral- or inversion-symmetric — a latent symmetry. Standard diagnostics then apply to the reduced chain: a filling-dependent topological number from the products of intracell versus intercell hoppings, real-space polarisation built from the position operator projected onto occupied states, and the divergence of the edge-state localisation length computed by transfer matrix. Both gapped and ungapped topological Anderson phases appear this way, extending the classification of disorder-induced topology beyond geometric symmetries and the tenfold way. The limitation is that the reduction is energy-dependent and demonstrated for one-dimensional chains whose adjacent blocks share exactly one site.