  We study the phase structure of the 3D nonlocal compact U(1) lattice gauge
theory coupled with a Higgs field by means of Monte-Carlo simulations. The
nonlocal interactions among gauge variables are along the temporal direction
and mimic the effect of local coupling to massless particles. We found that in
contrast to the 3D local abelian Higgs model which has only one phase, the
present model exhibits the confinement, Higgs, and Coulomb phases separated by
three second-order transition lines emanating from a triple point. This result
is quite important for studies on electron fractionalization phenomena in
strongly-correlated electron systems. Implications to them are discussed.
