It is shown that, an entire class of off-diagonally disordered linear lattices composed of two basic building blocks and described within a tight binding model can be tailored to generate absolutely continuous energy bands. It can be achieved if linear atomic clusters of an appropriate size are side coupled to a suitable subset of sites in the backbone, and if the nearest neighbor hopping integrals, in the backbone and in the side coupled cluster bear a certain ratio. We work out the precise relationship between the number of atoms in one of the building blocks in the backbone, and that in the side attachment. In addition, we also evaluate the definite correlation between the numerical values of the hopping integrals at different subsections of the chain, that can convert an otherwise point spectrum (or, a singular continuous one for deterministically disordered lattices) with exponentially (or power law ) localized eigenfunctions to an absolutely continuous spectrum comprising one or more bands (subbands) populated by extended, totally transparent eigenstates. The results, which are analytically exact, put forward a non-trivial variation of the Anderson localization [P. W. Anderson, Phys. Rev. 109, 1492 (1958)], pointing towards its unusual sensitivity to the numerical values of the system parameters and, go well beyond the other related models such as the Random Dimer Model (RDM) [Dunlap et al., Phys. Rev. Lett. 65, 88 (1990)].
Localization with non-Hermitian off-diagonal disorder
Harish-Chandra Research Institute, A CI of Homi Bhabha National Institute（哈拉·钱德拉研究所，霍米·巴巴国立学院下属机构）；Department of Theoretical Physics, Tata Institute of Fundamental Research（塔塔基础研究院理论物理系）
