Path-integral analysis of bosons interacting with a gauge field

Abstract

We analyze an effective action of bosons moving in a fluctuating gauge field, which describes the motion of the holons in the t-J model. The analysis is in terms of a dimensionless coupling constant g\ensuremath{\sim}24\ensuremath{\pi}t/J. We use a path-integral approach, which is a convenient method in the strong-coupling limit g\ensuremath{\gg}1. The effect of the gauge field is to suppress boson loops that enclose a large area, so that the main contribution comes from almost self-retracing paths. By taking a quenched average over the gauge field we are able to derive a renormalized density of states that has a shifted band edge, and that is enhanced near the band edge. We also find an expression for the diamagnetic susceptibility ${\mathrm{\ensuremath{\chi}}}_{\mathit{B}}$, that in the strong-coupling limit varies like ${\mathrm{\ensuremath{\chi}}}_{\mathit{B}}$\ensuremath{\sim}(gT${)}^{\mathrm{\ensuremath{-}}1}$, and is suppressed by a factor 0.2g compared to the weak-coupling limit. The enhanced density of states and the suppression of ${\mathrm{\ensuremath{\chi}}}_{\mathit{B}}$ both imply that Bose condensation is suppressed by the fluctuating gauge field. At lower temperatures the retracing path approximation breaks down, and one has to do a self-consistent calculation to determine ${\mathrm{\ensuremath{\chi}}}_{\mathit{B}}$. A numerical calculation shows that below ${\mathit{T}}_{\mathit{B}\mathit{E}}$\ensuremath{\sim}0.08${\mathit{T}}_{\mathit{B}\mathit{E}}^{0}$ the susceptibility ${\mathrm{\ensuremath{\chi}}}_{\mathit{B}}^{\mathrm{SC}}$ diverges exponentially.