Thermodynamics of Bose gases from functional renormalization with a hydrodynamic low-energy effective action

Abstract

The functional renormalization group for the effective action is used to construct an effective hydrodynamic description of weakly interacting Bose gases. We employ a scale-dependent parametrization of the boson fields developed previously to start the renormalization evolution in a Cartesian representation at high momenta and interpolate to an amplitude-phase one in the low-momentum regime. This technique is applied to Bose gases in one, two and three dimensions, where we study thermodynamic quantities such as the pressure and energy per particle. The interpolation leads to a very natural description of the Goldstone modes in the physical limit, and compares well to analytic and Monte-Carlo simulations at zero temperature. The results show that our method improves aspects of the description of low-dimensional systems, with stable results for the superfluid phase in two dimensions and even in one dimension.