Renormalised thermodynamics for Bose gases from low to critical temperatures

TL;DR

This paper develops a non-perturbative, renormalised thermodynamic framework for dilute Bose gases across temperature regimes, capturing critical behaviour and condensate depletion.

Contribution

It introduces a systematic renormalisation method for self-consistent 2PI approximations, extending beyond Gaussian theories like Hartree-Fock-Bogoliubov.

Findings

Determines condensate depletion across temperatures including critical point.

Calculates non-zero anomalous dimension at next-to-leading order.

Provides a consistent renormalised approach for thermodynamics of Bose gases.

Abstract

We compute thermodynamic properties of dilute Bose gases using non-perturbative approximations of the two-particle irreducible (2PI) effective action. It is shown how to systematically renormalise the self-consistent descriptions beyond conventional Gaussian approximations such as Hartree-Fock-Bogoliubov theory. This allows us to determine the condensate depletion from low to high temperatures, including its critical behaviour at the phase transition. While the universal anomalous dimension at criticality is vanishing for Gaussian approximations, we determine its non-zero value at next-to-leading order of a self-consistent expansion in the number of field components.