  We investigate the phase coherence time of weakly interacting tunneling
systems (TSs). We show that all neighbors of a given TS form together with the
TS of interest an entangled cluster as long as the linewidth of the excitation
of the neighbor is smaller than its interaction energy with the TS of interest.
Thus, the relaxation of all neighbors in the cluster contributes to the
dephasing of the TS of interest. This mechanism dominates the transversal decay
of the TSs and it explains recent two-pulse echo experiments in which the
exponential decay rate could not be explained within spectral diffusion
consistent with internal friction data. However, since the proposed mechanism
predicts only an exponential decay, the Gaussian like decay at short times
remains unexplained.
