  In this paper, we study a 3D compact U(1) lattice gauge theory with a variety
of nonlocal interactions that simulates the effects of gapless/gapful matter
fields. This theory is quite important to investigate the phase structures of
QED$_3$ and strongly-correlated electron systems like the 2D quantum spin
models, the fractional quantum Hall effect, the t-J model of high-temperature
superconductivity. We restrict the nonlocal interactions among gauge variables
only to those along the temporal direction and adjust their coupling constants
optimally to simulate the isotropic nonlocal couplings of the original models.
We perform numerical studies of the model to find that, for a certain class of
power-decaying couplings, there appears a second-order phase transition to the
deconfinement phase as the gauge coupling constant is decreased. On the other
hand, for the exponentially-decaying coupling, there are no signals for
second-order phase transition. These results indicate the possibility that
introduction of sufficient number of massless matter fields destabilizes the
permanent confinement in the 3D compact U(1) pure gauge theory due to
instantons.
