Condensate density of interacting bosons: a functional renormalization group approach

Abstract

We calculate the temperature dependent condensate density ${\rho }^0(T)$ of interacting bosons in three dimensions using the functional renormalization group (FRG). From the numerical solution of suitably truncated FRG flow equations for the irreducible vertices we obtain ${\rho }^0(T)$ for arbitrary temperatures. We carefully extrapolate our numerical results to the critical point and determine the order parameter exponent $\beta \approx 0.32$, in reasonable agreement with the expected value $0.345$ associated with the XY-universality class. We also calculate the condensate density in two dimensions at zero temperature using a truncation of the FRG flow equations based on the derivative expansion including cubic and quartic terms in the expansion of the effective potential in powers of the density. As compared with the widely used quadratic approximation for the effective potential, the coupling constants associated with the cubic and quartic terms increase the result for the condensate density by a few percent. However, the cubic and quartic coupling constants flow to rather large values, which sheds some doubt on FRG calculations based on a low order polynomial approximation for the effective potential.

9 pages, 6 figures

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• The nonperturbative functional renormalization group and its applications
• Universal thermodynamics of a two-dimensional Bose gas
• Functional renormalization group approach to interacting bosons at zero temperature
• Application of the functional renormalization group to Bose gases: from linear to hydrodynamic fluctuations
• Effective average action based approach to correlation functions at finite momenta
• Thermodynamics of Bose gases from functional renormalization with a hydrodynamic low-energy effective action
• Bogoliubov phonons in a Bose-Einstein condensate from the one-loop perturbative renormalization group