Superfluid Bose gas in two dimensions

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 $\ensuremath{\lambda}$ is logarithmic. Furthermore, for large $l$ the frequency dependence of the inverse propagator becomes quadratic. We find an upper bound for $\ensuremath{\lambda}$, and for large $\ensuremath{\lambda}$ 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 $l\ensuremath{\rightarrow}\ensuremath{\infty}$ logarithmically.