We prove that a disordered analog of the Su–Schrieffer–Heeger model exhibits dynamical localization (i.e., the fractional moment condition) at all energies except possibly zero energy, which is singled out by chiral symmetry. Localization occurs at arbitrarily weak disorder, provided it is sufficiently random. If furthermore the hopping probability measures are properly tuned so that the zero energy Lyapunov spectrum does not contain zero, then the system exhibits localization also at that energy, which is of relevance for topological insulators. The method also applies to the usual Anderson model on the strip.
To be compatible with the rest of this paper, we denote a size of a matrix here by L instead of the usual N in the literature; the usual name of the conjecture is “the conjecture.”