2-DIMENSIONAL BOSE-LIQUID WITH STRONG GAUGE-FIELD INTERACTION

Two unrelated problems can be reduced to a model of a Bose gas interac ting with a gauge field: (i) the effect of thermal fluctuations on a s ystem of vortices in bulk superconductors in fields H(c1) much less th an H much less than H(c2), and (ii) charged, spinless excitations in t wo-dimensional (2D) strongly correlated electron systems. Both problem s are important for the theory of high-temperature superconductors. We study this model in three regimes: at finite temperatures, assuming t hat the gauge field is purely transverse; at T = 0, for the purely sta tic (2D Coulomb) interaction; and at T = 0, for a weak Coulomb interac tion and a strong transverse one. Transverse interactions suppress the temperature of the superfluid transition significantly. A sufficientl y strong transverse interaction is shown to produce a phase separation as the temperature decreases (in the absence of Coulomb repulsion). I f there is Coulomb repulsion, the ground state does not have off-diago nal long-range order but the superfluid density is not zero unless the Coulomb constant exceeds a critical value. Sufficiently strong coupli ng to the transverse field destroys superfluidity as well. In the norm al state formed at large couplings, the translational invariance is in tact. We propose a bosonic ground state that is not superfluid at T = 0. We discuss the implications of these results both for vortex liquid s and strongly correlated electron systems.