We investigate the two-dimensional Hubbard model with next-nearest-neighbor hopping, t′, using the dynamical cluster approximation. We confirm the existence of a first-order phase-separation transition terminating at a second-order critical point at filling nc(t′) and temperature Tps(t′). We find that as t′ approaches zero, Tps(t′) vanishes and nc(t′) approaches the filling associated with the quantum critical point separating the Fermi liquid from the pseudogap phase. We propose that the quantum critical point under the superconducting dome is the zero-temperature limit of the line of second-order critical points.
Ehsan Khatami, K. Mikelsons, D. Galanakis, A. Macridin, J. Moreno, R. Scalettar, and M. Jarrell. "Quantum criticality due to incipient phase separation in the two-dimensional Hubbard model" Physical Review B (2010). doi:10.1103/PhysRevB.81.201101