Self-consistent Hartree-Fock-Bogoliubov approach for bosons: self-eliminating divergence and pure pair condensate

TL;DR

This paper develops a self-consistent Hartree-Fock-Bogoliubov method for interacting Bose gases that removes divergence issues and reveals a stable mixture of single-particle and pair condensates, predicting higher transition temperatures.

Contribution

It introduces a divergence-free, self-consistent HFB solution for bosons that accounts for pair condensates and compares thermodynamic predictions with the Popov approximation.

Findings

The HFB approach predicts higher transition temperatures than the Popov approximation.

Pure pair condensates are unstable, favoring a mixture with single-particle condensates.

The method intrinsically eliminates divergence in the HFB equations.

Abstract

We investigate the thermodynamic properties of an interacting Bose gas with a condensate within the energy-functional formulation of the Hartree-Fock-Bogoliubov (HFB) approach. For a contact interaction, we derive a self-consistent solution to the HFB equations that intrinsically eliminates divergence. This solution characterizes the equilibrium state featuring a condensate of correlated pairs of particles. We analyze the temperature dependence of key thermodynamic quantities such as condensate density, chemical potential, entropy, pressure, specific heat capacity at constant volume, and isothermal compressibility and compare them with predictions from the Popov approximation (PA). We predict that the transition temperature shifts to higher values due interactions, with the HFB approach yielding a larger shift than the PA. Analysis of the compressibility indicates that a pure pair condensate is unstable, and the stable equilibrium corresponds to only a mixture of single-particle and pair condensates.