Abelian two-Higgs model of strongly correlated electrons: Phase structure, strengthening of phase transition, and QCD at finite density

Abstract

We investigate nonperturbative features of a three-dimensional Abelian Higgs model with singly and doubly charged scalar fields coupled to a single compact Abelian gauge field. The model is pretending to describe various planar systems of strongly correlated electrons such as high-T{sub c} superconductivity in the overdoped regime and exotic materials possessing excitations with fractionalized quantum numbers. The complicated phase structure of the model is studied thoroughly using numerical tools and analytical arguments. In the three-dimensional space of coupling parameters we identify the Fermi liquid, the spin gap, the superconductor and the strange metallic phases. The behavior of three kinds of topological defects--holon, spinon vortices, and monopoles--is explored in various phases. We also observe an effect, the strong enhancement of the phase transition strength reflected in a lower order of the transition: at sufficiently strong gauge coupling the two second-order phase transitions--corresponding to spinon pair and holon condensation lines--join partially in the phase diagram and become a first-order phase transition in that region. The last observation may have an analog in quantum chromodynamics at nonzero temperature and finite baryon density. We argue that at sufficiently large baryon density the finite-temperature transition between the (three-flavor paired) color superconducting phase and the quark-gluonmore » plasma phases should be much stronger compared with the transition between two-flavor paired and three-flavor paired superconducting phases.« less