The Kosterlitz-Thouless-Berezinskii transition of homogeneous and trapped Bose gases in two dimensions

TL;DR

This paper derives the transition temperature and superfluid properties of 2D Bose gases, both homogeneous and trapped, highlighting how interactions influence the Kosterlitz-Thouless transition and differ from ideal Bose-Einstein condensation.

Contribution

It provides a diagrammatic perturbation theory derivation of the KTB transition temperature and analyzes the effects of trapping and interactions on the transition.

Findings

Critical temperature $T_{KT}$ derived for homogeneous gases.

Interaction effects lower the transition temperature in trapped gases.

Superfluid mass jump is suppressed in trapped systems.

Abstract

We derive the scaling structure of the Kosterlitz-Thouless-Berezinskii (KTB) transition temperature of a homogeneous Bose gas in two dimensions within diagrammatic perturbation theory. Approaching the system from above the transition, we calculate the critical temperature, $T_{KT}$, and show how the superfluid mass density emerges from Josephson's relation as an interplay between the condensate density in a finite size system, and the infrared structure of the single particle Green's function. We then discuss the trapped two-dimensional Bose gas, where the interaction changes the transition qualitatively from Bose-Einstein in an ideal gas to a KTB transition in the thermodynamic limit. We show that the transition temperature lies below the ideal Bose-Einstein transition temperature, and calculate the first correction in terms of the interparticle interactions. The jump of the total superfluid mass at the transition is suppressed in a trapped system.