Numerical studies on the Anderson localization problem

The Anderson localization transition has been studied by numerical methods for very large two- and three-dimensional samples with up to 30 000 sites, varying both the energy and the strength of disorder of the electronic system, which is described by a tight-binding Hamiltonian with both diagonal and off-diagonal disorder. By an orthogonal transformation, the system is mapped numerically onto an equivalent semi-infinite chain. This transformation allows not only for a real-space renormalization by decimation, which is numerically exact, but also for a calculation of eigenstates, various Green's functions, and finally also for an evaluation of the conductivity directly from the Kubo formula.