  We study the phase structure of a three dimensional Abelian Higgs model with
singly- and doubly-charged scalar fields coupled to a compact Abelian gauge
field. The model is pretending to describe systems of strongly correlated
electrons such as high-Tc superconductivity in overdoped regime and exotic
phases supporting excitations with fractionalized quantum numbers. We identify
the Fermi liquid, the spin gap, the superconductor and the strange metallic
phases in which densities and properties of holon and spinon vortices and
monopoles are explored. The phase diagram in the 3D coupling space is
predicted. We show that at sufficiently strong gauge coupling the spinon-pair
and holon condensation transitions merge together and become, unexpectedly,
first order.
