In this work, we build upon the theoretical framework developed in our previous study Phys. Lett. A 523, 129787 (2024), where the Cornwall–Jackiw–Tomboulis effective action formalism was applied to a dilute Bose gas, to investigate its thermodynamic properties in the condensed phase at sufficiently low temperatures within the improved Hartree–Fock approximation. We focus on the analyses of the chemical potential, pressure, energy density, and specific heat at constant volume, which are derived within a unified, self-consistent, and gapless framework. The results obtained show excellent agreement with those predicted by the Hartree–Fock–Bogoliubov theory in the appropriate limits. Remarkably, our results demonstrate universal behavior for the reduced thermodynamic quantities, and a comparison with available experimental data for the chemical potential is made.
Thu et al. (Thu,) studied this question.