Superfluid Bose gas in two dimensions

TL;DR

This paper studies two-dimensional Bose gases, revealing how interactions evolve across scales, the nature of condensate depletion, and the phase transition behavior, especially near the Kosterlitz-Thouless transition.

Contribution

It provides a detailed analysis of the scale dependence of interactions and phase transition characteristics in 2D Bose gases using the functional renormalization group.

Findings

Interaction strength $mbda$ has a logarithmic scale dependence.

Deviations from Bogoliubov theory are significant at large $mbda$.

Critical temperature $T_c/n$ vanishes logarithmically as scale increases.

Abstract

We investigate Bose-Einstein condensation for ultracold bosonic atoms in two-dimensional systems. The functional renormalization group for the average action allows us to follow the effective interactions from molecular scales (microphysics) to the characteristic extension of the probe $l$ (macrophysics). In two dimensions the scale dependence of the dimensionless interaction strength $\lambda$ is logarithmic. Furthermore, for large $l$ the frequency dependence of the inverse propagator becomes quadratic. We find an upper bound for $\lambda$, and for large $\lambda$ substantial deviations from the Bogoliubov results for the condensate depletion, the dispersion relation and the sound velocity. The melting of the condensate above the critical temperature $T_c$ is associated to a phase transition of the Kosterlitz-Thouless type. The critical temperature in units of the density, $T_c/n$, vanishes for $l\to\infty$ logarithmically.