Numerical-renormalization-group approach to Anderson localization.

We have studied the behavior of the conductance in large disordered systems using a numerical real-space renormalization-group (RG) technique. Using a distribution of scattering matrices as the fundamental building blocks of our system, very large structures can be studied by combining the blocks in the appropriate way and performing a RG step at each stage. The method is sufficiently general that it allows several RG techniques to be used and thus be compared with one another. We examine the conductance behavior in two and three dimensions with increasing system size for different shaped building blocks and different initial disorders. We compare the results with other work. Our results are extremely sensitive to the detailed implementation of each RG method used and therefore we suggest that all localization results obtained via RG methods must be interpreted with caution.