  Coherence in electronic interferometers is typically believed to be restored
fully in the limit of small voltages, frequencies and temperatures. However, it
is crucial to check this essentially perturbative argument by nonperturbative
methods. Here, we use the numerical renormalization group to study ac transport
and decoherence in an experimentally realizable model interferometer, a
parallel double quantum dot coupled to a phonon mode. The model allows to
clearly distinguish renormalization effects from decoherence. We discuss finite
frequency transport and confirm the restoration of coherence in the dc limit.
