Flat-band localization in weakly disordered system

We present a detailed analysis of the insulator-metal-insulator transition of a disordered system, starting from a characteristic three-dimensional system possessing highly degenerated localized eigenstates. The finite-size scaling of level statistics and multifractal analysis for systems larger than those in the previous study show the transition points more clearly. We clarify whether the eigenstates are indeed localized or extended at several energies for several strengths of disorder by examining also the inverse participation ratio of the wave functions. In particlular, we clarify that the localization for weak disorder is different from the ordinary one in the sense that the strength of localization is independent of the strength of disorder. The localization persists even when the strength of disorder is numerically as small as possible, 10(-13) in our present numerical study.