Application of the functional renormalization group to Bose gases: from linear to hydrodynamic fluctuations

TL;DR

This paper employs the functional renormalization group with a hydrodynamic approach to analyze weakly interacting Bose gases, successfully describing superfluid phases and matching Monte Carlo results in two and three dimensions.

Contribution

It introduces a scale-dependent parametrization of boson fields that bridges Cartesian and amplitude-phase representations, enabling consistent infrared descriptions of Bose gases.

Findings

Stable superfluid phase at finite temperature in 2D.

Good agreement with Monte Carlo simulations.

Effective description of infrared regimes in 2D and 3D.

Abstract

We study weakly interacting Bose gases using the functional renormalization group with a hydrodynamic effective action. We use a scale-dependent parametrization of the boson fields that interpolates between a Cartesian representation at high momenta and an amplitude-phase one for low momenta. We apply this to Bose gases in two and three dimensions near the superfluid phase transition where they can be described by statistical O(2) models. We are able to give consistent physical descriptions of the infrared regime in both two and three dimensions. In particular, and in contrast to previous studies using the functional renormalization group, we find a stable superfluid phase at finite temperatures in two dimensions. We compare our results for the superfluid and boson densities with Monte-Carlo simulations, and we find they are in reasonable agreement.