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We explore the momentum-sector-selective metal insulator transitions recentlyfound in the eight - site dynamical cluster approximation to thetwo-dimensional Hubbard model. The phase diagram in the space of interactionand second-neighbor hopping is established. The initial transitions fromFermi-liquid like to sector-selective phases are found to be of second order,caused by the continuous opening of an energy gap whereas the other transitionsare found to be of first order. In the sector-selective phase the Fermi surfaceregions which are not gapped are found to have a non-Fermi-liquid self-energy.We demonstrate that the phenomenon is not caused by the Van Hove divergence inthe density of states. The sector-selective and insulating phases arecharacterized by a cluster spin correlation function that is strongly peaked atthe commensurate antiferromagnetic wave vector $(\pi,\pi)$ but the model has nonematic instability. Comparison to dynamical mean-field studies on smallerclusters is made.

Momentum-sector-selective metal-insulator transition in the eight-site dynamical mean-field approximation to the Hubbard model in two dimensions