Superfluidity in the two-dimensional gauge-field model: A renormalization-group analysis

Abstract

We study an effective action of bosons interacting with a gauge field, which is derived from the t-J model in the slave-boson approach. We use a renormalization-group (RG) scheme to calculate the temperature ${\mathit{T}}_{\mathrm{BE}}$ below which the bosons start to condense in a superfluid state. One expects that a strongly fluctuating gauge field tends to destroy this superfluid state. Our numerical calculations indeed show that the presence of a gauge field suppresses the onset of superfluidity. This suppression is partly due to quantum fluctuations, and partly due to thermal excitations of the gauge field. An analytical calculation of the flow in the classical regime T(l)\ensuremath{\gg}1 shows that our perturbative RG scheme provides an expansion of the suppression of ${\mathit{T}}_{\mathrm{BE}}$ in powers of ${\mathit{q}}_{00}^{2}$/${\mathit{u}}_{0}$, where ${\mathit{q}}_{00}^{2}$ is the coupling constant of the gauge field, and ${\mathit{u}}_{0}$ is the short-range repulsion between the bosons. The RG scheme breaks down if ${\mathit{q}}_{00}^{2}$/${\mathit{u}}_{0}$\ensuremath{\gtrsim}1, in which case one gets into the strong-coupling limit. Thus unfortunately the RG scheme is not reliable for the strong-coupling problem, which is appropriate for the t-J model with t/J\ensuremath{\sim}1.