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

摘要

We investigate non-perturbative features of a three-dimensional Abelian Higgsmodel with singly- and doubly-charged scalar fields coupled to a single compactAbelian gauge field. The model is pretending to describe various planar systemsof strongly correlated electrons such as high-Tc superconductivity in theoverdoped regime and exotic materials possessing excitations withfractionalized quantum numbers. The complicated phase structure of the model isstudied thoroughly using numerical tools and analytical arguments. In thethree-dimensional space of coupling parameters we identify the Fermi liquid,the spin gap, the superconductor and the strange metallic phases. The behaviorof three kinds of topological defects -- holon and spinon vortices andmonopoles - is explored in various phases. We also observe a new effect, thestrong enhancement of the phase transition strength reflected in a lower orderof the transition: at sufficiently strong gauge coupling the two second orderphase transitions -- corresponding to spinon-pair and holon condensation lines- join partially in the phase diagram and become a first order phase transitionin that region. The last observation may have an analogue in QuantumChromodynamics at non-zero temperature and finite baryon density. We argue thatat sufficiently large baryon density the finite-temperature transition betweenthe (3-flavor paired) color superconducting phase and the quark-gluon plasmaphases should be much stronger compared with the transition between 2-flavorpaired and 3-flavor paired superconducting phases.