A simple approach to Anderson localization in one-dimensional disordered lattices

We present a simple approach to Anderson localization in one-dimensional disordered lattices. We introduce the tight-binding model in which one orbital and a single random energy are assigned to each lattice site, and the hopping integrals are constant and restricted to nearest-neighbor sites. The localization of eigenstates is explained by two-parameter scaling arguments. We compare the size scaling of the level spacing in the bare energy spectrum of the quasi-particle (in the ideal lattice) with the size scaling of the renormalized disorder seen by the quasi-particle. The former decreases faster than the latter with increasing system size, giving rise to mixing and to the localization of the bare quasi-particle wave functions in the thermodynamic limit. We also provide a self-consistent calculation of the localization length and show how this length can be obtained from optical absorption spectra for Frenkel excitons.