Flat bands by latent symmetry

The geometry of a lattice may cause energy eigenstates to localize compactly by destructive interference, resulting in flat bands. This effect is often induced symmetry. A ``latent'' symmetry, inspired from graph theory, hidden permutation symmetry revealed upon reduction the original system onto subsystem; here, an effective two-site dimer. Combined with collective symmetries between possible pathways connecting dimer sites special site subsets unit cell, latent provides novel systematic way explore and construct