An Abelian two-Higgs model and high temperature superconductivity

We study a three dimensional Abelian Higgs model containing singly- and doubly-charged scalar fields coupled to a compact Abelian gauge field in the London limit. The model attracts interest because of its relevance to high-Tc superconductors with charge 1 holon and charge 2 spinon-pair fields. It contains two types of vortices carrying magnetic flux and one type of instanton-like monopoles. Using thermodynamic and topological observables we present the phase diagram in the parameter space of the gauge and holon and spinon-pair couplings. The Fermi liquid, the spin gap, the superconductor and the strange metallic phases have been identified in a wide region of parameters. The model may serve as a toy system modelling non-perturbative properties of the Yang-Mills theory.