  We argue that symmetry-broken phases proximate in phase space to
symmetry-protected topological phases can exhibit dynamical signatures of
topological physics. This dynamical, symmetry-protected "topological" regime is
characterized by anomalously long edge coherence times due to the topological
decoration of quasiparticle excitations, even if the underlying
zero-temperature ground state is in a non-topological, symmetry-broken state.
The dramatic enhancement of coherence can even persist at infinite temperature
due to prethermalization. We find exponentially long edge coherence times that
are stable to symmetry-preserving perturbations, and not the result of
integrability.
