Pseudogap and the specific heat of high T$_c$ superconductors: a Hubbard model in a n-pole approximation

In this work the specific heat of a two-dimensional Hubbard model, suitable to discuss high-$T_c$ superconductors (HTSC), is studied taking into account hopping to first ($t$) and second ($t_2$) nearest neighbors. Experimental results for the specific heat of HTSC's, for instance, the YBCO and LSCO, indicate a close relation between the pseudogap and the specific heat. In the present work, we investigate the specific heat by the Green's function method within a $n$-pole approximation. The specific heat is calculated on the pseudogap and on the superconducting regions. In the present scenario, the pseudogap emerges when the antiferromagnetic (AF) fluctuations become sufficiently strong. The specific heat jump coefficient $\Delta \gamma$ decreases when the total occupation per site ($n_T$) reaches a given value. Such behavior of $\Delta \gamma$ indicates the presence of a pseudogap in the regime of high occupation.