Auxiliary field approach to dilute Bose gases with tunable interactions

TL;DR

This paper introduces the LOAF auxiliary field method for dilute Bose gases, providing a conserving mean-field approximation that accurately describes phase transitions and critical behavior across interaction strengths.

Contribution

The paper develops the LOAF theory using auxiliary fields, offering a consistent, higher-order loop expansion framework for dilute Bose gases with tunable interactions.

Findings

LOAF predicts a second-order phase transition.

LOAF results align with Popov approximation in certain regimes.

The method enables exploration of the critical regime at all coupling strengths.

Abstract

We rewrite the Lagrangian for a dilute Bose gas in terms of auxiliary fields related to the normal and anomalous condensate densities. We derive the loop expansion of the effective action in the composite-field propagators. The lowest-order auxiliary field (LOAF) theory is a conserving mean-field approximation consistent with the Goldstone theorem without some of the difficulties plaguing approximations such as the Hartree and Popov approximations. LOAF predicts a second-order phase transition. We give a set of Feynman rules for improving results to any order in the loop expansion in terms of composite-field propagators. We compare results of the LOAF approximation with those derived using the Popov approximation. LOAF allows us to explore the critical regime for all values of the coupling constant and we determine various parameters in the unitarity limit.