Interplay Between Condensation Energy, Pseudogap, and the Specific Heat of a Hubbard Model in a n-Pole Approximation

The condensation energy and the specific heat jump of a two-dimensional Hubbard model, suitable to discuss high-\(T_c\) superconductors, are studied. In this work, the Hubbard model is investigated by the Green’s function method within a \(n\)-pole approximation, which allows to consider superconductivity with \(d_{x^2-y^2}\)-wave pairing. In the present scenario, the pseudogap regime emerges when the antiferromagnetic correlations become sufficiently strong to move to lower energies the region around of the nodal point \((\pi ,\pi )\) on the renormalized bands. It is observed that above a given total occupation \(n_T\), the specific heat jump \(\Delta C\) and also the condensation energy \(U(0)\) decrease signaling the presence of the pseudogap.