Numerical signatures of disordered topological phases

We investigate a number of numerical signatures which distinguish the topological and trivial phases of clean and disordered insulators. In particular, we consider two dimensional systems and suggest a procedure for numerically constructing a sequence of maximally localized mutually orthogonal states which span the Hilbert space. The localization lengths of states constructed using our procedure is numerically shown to diverge as a power law for systems with non-zero Chern number, and conversely saturate for systems with zero Chern number. We construct and numerically verify a scaling argument which suggests this exponent is universal. Finally, we discuss extensions of this approach to other spatial dimensions and symmetry classes.