  We investigate the collapse and revival of first-order coherence in deep
optical lattices when long-range interactions are turned on, and find that the
first few revival peaks are strongly attenuated already for moderate values of
the nearest-neighbor interaction coupling. It is shown that the conventionally
employed Gutzwiller wavefunction, with only onsite-number dependence of the
variational amplitudes, leads to incorrect predictions for the collapse and
revival oscillations. We provide a modified variant of the Gutzwiller ansatz,
reproducing the analytically calculated time dependence of first-order
coherence in the limit of zero tunneling.
