Phase separation in Hubbard model

We investigate the phase separation in the Hubbard model by employing the dynamical cluster approximation. We find that an enhanced compressibility in the underdoped regime is a general characteristic of the Hubbard model for the most regions of the parameter space. Moreover, a next-nearest-neighbor hopping $t'$ corresponding to electron-doped cuprates will drive a finite temperature transition into a phase separated state consisting of an undoped phase and a rich doped one. A Coulomb repulsion $U\agt W$ is a necessary condition for the transition to take place. Phase separation and charge ordering scenarios for high $T_c$ are becoming increasingly relevant in the highlight of the recent experiments which reveal that charge modulation is an intrinsic characteristic of hole-doped cuprates. We find that phase separation is more prevalent when $t'>0$, consistent with the electron-doped cuprates.