Phase diagram for interacting Bose gases

TL;DR

This paper introduces a new inversion method using self-energy expansion to map the phase diagram of Bose-Einstein condensation in interacting gases, providing improved theoretical predictions aligned with Monte Carlo data.

Contribution

It presents a novel approach to determine the phase diagram of interacting Bose gases using a self-energy expansion and introduces a new condensation condition based on the T-matrix pole.

Findings

Self-consistent T-matrix yields a critical temperature coefficient close to Monte Carlo data.

Screened ladder approximation improves the description of the phase transition.

Non-selfconsistent T-matrix overestimates the critical temperature coefficient.

Abstract

We propose a new form of the inversion method in terms of a selfenergy expansion to access the phase diagram of the Bose-Einstein transition. The dependence of the critical temperature on the interaction parameter is calculated. This is discussed with the help of a new condition for Bose-Einstein condensation in interacting systems which follows from the pole of the T-matrix in the same way as from the divergence of the medium-dependent scattering length. A many-body approximation consisting of screened ladder diagrams is proposed which describes the Monte Carlo data more appropriately. The specific results are that a non-selfconsistent T-matrix leads to a linear coefficient in leading order of 4.7, the screened ladder approximation to 2.3, and the selfconsistent T-matrix due to the effective mass to a coefficient of 1.3 close to the Monte Carlo data.