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

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.