  We revisit the problem of decoherence of a qubit centrally coupled to an
interacting spin environment, here modeled by a quantum compass chain or an
extended XY model in a staggered magnetic field. These two models both support
distinct spin liquid phases, adding a new element to the problem. By analyzing
their Loschmidt echoes when perturbed by the qubit we find that a fast
decoherence of the qubit is conditioned on the presence of propagating
quasiparticles which couple to it. Different from expectations based on earlier
works on central spin models, our result implies that the closeness of an
environment to a quantum phase transition is neither a sufficient nor a
necessary condition for an accelerated decoherence rate of a qubit.
