Functional renormalization for Bose-Einstein Condensation

TL;DR

This paper applies functional renormalization to analyze Bose-Einstein condensation in interacting bosons, providing insights into fluctuation effects, phase diagrams, and critical temperature shifts, with results aligning well with known theories.

Contribution

It introduces a functional renormalization approach to study Bose-Einstein condensation, extending beyond Bogoliubov approximation and analyzing fluctuation effects at various temperatures.

Findings

Bound on scattering length for dilute gases

Deviation in critical temperature from free theory

Agreement of sound velocity with Bogoliubov theory

Abstract

We investigate Bose-Einstein condensation for interacting bosons at zero and nonzero temperature. Functional renormalization provides us with a consistent method to compute the effect of fluctuations beyond the Bogoliubov approximation. For three dimensional dilute gases, we find an upper bound on the scattering length a which is of the order of the microphysical scale - typically the range of the Van der Waals interaction. In contrast to fermions near the unitary bound, no strong interactions occur for bosons with approximately pointlike interactions, thus explaining the high quantitative reliability of perturbation theory for most quantities. For zero temperature we compute the quantum phase diagram for bosonic quasiparticles with a general dispersion relation, corresponding to an inverse microphysical propagator with terms linear and quadratic in the frequency. We compute the temperature dependence of the condensate and particle density n, and find for the critical temperature T_c a deviation from the free theory, Delta T_c/T_c = 2.1 a n^{1/3}. For the sound velocity at zero temperature we find very good agreement with the Bogoliubov result, such that it may be used to determine the particle density accurately.