Incomplete Localization for Disordered Chiral Strips

TL;DR

This paper proves that a disordered chiral model exhibits dynamical localization at all energies except possibly zero, with localization at zero energy achievable under certain conditions, relevant for topological insulators.

Contribution

It establishes localization properties for disordered chiral strips, including at zero energy under specific conditions, extending understanding of topological insulator models.

Findings

Localization at all energies except possibly zero.

Localization at zero energy under tuned conditions.

Applicability to the Anderson model on the strip.

Abstract

We prove that a disordered analog of the Su-Schrieffer-Heeger model exhibits dynamical localization (i.e. the fractional moments 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.