Extended states in disordered one-dimensional systems in the presence of the generalized N -mer correlations

We have been investigating the problem of the Anderson localization in a disordered one-dimensional tight-binding model. The disorder is created by the interaction of mobile particles with other species, immobilized at random positions. We introduce a method of creating correlations in the optical lattices with such a kind of disorder by using two different lattices with commensurate lattice lengths to hold two species of the particles. Such a model, called the generalized random N-mer model, leads to the appearance of multiple extended states in contrast to a localization of all states usually expected in one dimension. We develop a method, based on properties of transfer matrices which can be used to determine the presence of extended states and their energies for that class of correlations. Analytical results are compared with the numerical calculations for several cases which can be realized in cold-atom experiments.