Localization and level statistics in a one-dimensional solid state model with periodically modulated potential

For a solid state model described by a band matrix with diagonal elements depending periodically on the siteindex we determine the eigenstates and their localization length. The periodicity of the diagonal elements gives rise to the appearance of a pronounced peak structure of the eigenstates with the same period. The same type of peak-structure is present in the quasi-energy states of some periodically driven quantum systems, and can be associated with a nearly conversed quasi-momentum quantum number. We investigate the influence of the periodic peak structure on the nearest neighbor level spacing distribution and find that the nearly conserved quasi-momentum modifies but does not destroy the level repulsion expected for a Gaussian orthogonal ensemble.