Non-perturbative predictions for cold atom Bose gases with tunable interactions

TL;DR

This paper develops a non-perturbative theoretical framework for dilute Bose gases with tunable interactions, accurately capturing phase transition properties and critical temperatures across a wide range of coupling strengths.

Contribution

It introduces a loop expansion using composite-field propagators that effectively describes Bose gases non-perturbatively, satisfying key physical theorems and matching known weak-coupling results.

Findings

Describes a large interval of coupling constants successfully.

Satisfies Goldstone's theorem and predicts a second-order Bose-Einstein transition.

Aligns with weak-coupling critical temperature predictions.

Abstract

We derive a theoretical description for dilute Bose gases as a loop expansion in terms of composite-field propagators by rewriting the Lagrangian in terms of auxiliary fields related to the normal and anomalous densities. We demonstrate that already in leading order this non-perturbative approach describes a large interval of coupling-constant values, satisfies Goldstone's theorem, yields a Bose-Einstein transition that is second-order, and is consistent with the critical temperature predicted in the weak-coupling limit by the next-to-leading order large-N expansion.