Hidden Bose-Einstein Singularities in Correlated Electron Systems: III. Thermodynamic Signals

We study thermodynamic consequences of the hidden Bose-Einstein singularities, which have been predicted to cause a pseudogap phase, based on quantum field theory of ordered phases. Starting from the Luttinger-Ward functional for the grand thermodynamic potential, we derive expressions of the Helmholtz free energy, internal energy, entropy, and heat capacity in a form suitable for numerical studies. They are applied to the weakly attractive Hubbard model in three dimensions to calculate the thermodynamic potentials numerically and continuously for the normal, pseudogap, and superconducting phases on the same footing. It is shown that the entry into the pseudogap phase is detectable as singularities of thermodynamic potentials, especially a discontinuity in the heat capacity.