Compressibility of a two-dimensional extended Hubbard model
  The compressibility of an extended $d-p$ Hubbard model is investigated by the Roth's two-pole approximation. Using the factorization procedure proposed by Beenen and Edwards, superconductivity with singlet $d_{x^2-y^2}$-wave pairing is also considered. Within this framework, the effects of $d-p$ hybridization and Coulomb interaction $U$ on the compressibility are studied carefully. It has been found that the compressibility diverges and then it becomes negative near the half-filling. Within Roth's method, it has been verified that an important contribution for the negative compressibility comes from the spin-correlation term $<S_j^+S_i^->$ present in Roth's band shift. This correlation function plays an important role due to its high doping dependence. Also, its effects in the band shift and consequently in the compressibility are pronounced near the half-filling. The numerical results show that the hybridization acts in the sense of suppressing the negative compressibility near half-filling. Finally, the possibility of a connection between the negative compressibility and the phase separation is also discussed. 
E. J. Calegari, S. G. Magalh\~aes and A A. Gomes