  We introduce a 3D compact U(1) lattice gauge theory having nonlocal
interactions in the temporal direction, and study its phase structure. The
model is relevant for the compact QED$_3$ and strongly correlated electron
systems like the t-J model of cuprates. For a power-law decaying long-range
interaction, which simulates the effect of gapless matter fields, a
second-order phase transition takes place separating the confinement and
deconfinement phases. For an exponentially decaying interaction simulating
matter fields with gaps, the system exhibits no signals of a second-order
transition.
