  We explore the momentum-sector-selective metal insulator transitions recently
found in the eight - site dynamical cluster approximation to the
two-dimensional Hubbard model. The phase diagram in the space of interaction
and second-neighbor hopping is established. The initial transitions from
Fermi-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 transitions
are found to be of first order. In the sector-selective phase the Fermi surface
regions 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 in
the density of states. The sector-selective and insulating phases are
characterized by a cluster spin correlation function that is strongly peaked at
the commensurate antiferromagnetic wave vector $(\pi,\pi)$ but the model has no
nematic instability. Comparison to dynamical mean-field studies on smaller
clusters is made.
