Numerical signatures of topology in disordered insulators*

We investigate a number of numerical signatures which distinguish the topological and trivial phases of disordered insulators. In particular, we consider three dimensional systems with time-reversal symmetry (class AII) and numerically construct a set of maximally commuting spin-like operators using local unitary circuits. The properties of the resulting spin operators may be used to identify the topology of the underlying phase. Using similar methods, we also construct analogues of Wannier functions for disordered systems with symmetry. Finally, we discuss extensions of this approach to other spatial dimensions and symmetry classes.