  We study the behavior of several physical properties of the Haldane model as
the system undergoes its transition from the normal-insulator to the
Chern-insulator phase. We find that the density matrix has exponential decay in
both insulating phases, while having a power-law decay, more characteristic of
a metallic system, precisely at the phase boundary. The total spread of the
maximally-localized Wannier functions is found to diverge in the
Chern-insulator phase. However, its gauge-invariant part, related to the
localization length of Resta and Sorella, is finite in both insulating phases
and diverges as the phase boundary is approached. We also clarify how the usual
algorithms for constructing Wannier functions break down as one crosses into
the Chern-insulator region of the phase diagram.
