A functional renormalization group approach to thermodynamics of weakly interacting Bose gases: from linear to hydrodynamic fluctuations

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 developed previously that interpolates between a Cartesian representation at high momenta and an amplitude-phase one for low momenta. We apply this to Bose gases in one, two and three dimensions. We study thermodynamic quantities such as the pressure and energy per particle, with surprisingly stable results even for the difficult case of one dimension. The interpolation between the two limits leads to a very natural approach to the physical limit, which compares favorably to analytic and Monte-Carlo simulations. The results shows that our method is a very good general purpose approach to the many-body theory of such systems.