  A local Hamiltonian with Topological Quantum Order (TQO) has a robust ground
state degeneracy that makes it an excellent quantum memory candidate. This
memory can be corrupted however if part of the state leaves the protected
ground state manifold and returns later with a dynamically accrued phase error.
Here we analyse how TQO suppresses this process and use this to quantify the
degree to which spectral densities in different topological sectors are
correlated. We provide numerical verification of our results by modelling an
interacting p-wave superconducting wire.
