Density of states and magnetic susceptibilities on the octagonal tiling

We study electronic properties as a function of the six types of local environments found in the octagonal tiling. The density of states has six characteristic forms, although the detailed structure differs from site to site since no two sites are equivalent in a quasiperiodic tiling. We present the site-dependent magnetic susceptibility of electrons on this tiling, which also has six characteristic dependences. We show the existence of a non-local spin susceptibility, which decays with the square of the distance between sites and is the quasiperiodic version of Ruderman-Kittel oscillations. These results are obtained for a tight-binding Hamiltonian with pure hopping.Finally, we investigate the formation of local magnetic moments when electron-electron interactions are included. PACS Nos: 61.44+p,71.20C,71.25,75.10L This study of a tight-binding model on the two dimensional quasiperiodic tiling with eight-fold symmetry, the octagonal tiling, is aimed at understanding electronic properties in real space. There is not much known about quasiperiodic Hamiltonians in two and higher dimensions. To date, studies on quasiperiodic tight-binding models have focused on the form of the density of states, on the response of energy levels to changes of boundary condition (which gives a measure of the degree of localization of the wavefunctions), and on the conductance of such tilings (reviewed in [1]). These studies are important for understanding experiments on transport phenomena, and for resolving whether quasicrystals are intrinsically metals or insulators. However the properties studied are site-averaged properties, and are characteristic of the tiling as a whole. Quasicrystals are interesting for their local properties as well, since they allow local