  Cluster dynamical mean field calculations based on 2, 4, 8 and 16 site
clusters are used to analyze the doping-driven metal-insulator transition in
the two dimensional Hubbard model. Comparison of results obtained on different
clusters enables a determination of those aspects of the physics that are
common to all clusters and permits identification of artifacts associated with
particular cluster geometries. A modest particle-hole asymmetry in the
underlying band structure is shown to lead to qualitatively different behavior
on the hole doped side than on the electron doped side. For particle-hole
asymmetry of the sign and magnitude appropriate to high-$T_c$ cuprates, the
approach to the insulator from the hole-doping side is found to proceed in two
stages from a high-doping region where the properties are those of a Fermi
liquid with moderately renormalized parameters and very weak momentum
dependence. As doping is reduced the system first enters an intermediate doping
regime where the Fermi liquid renormalizations are larger and the electron self
energy varies significantly around the Fermi surface and then passes to a small
doping regime characterized by a gap in some regions of the Fermi surface but
gapless behavior in other regions. On the electron doped side the partially
gapped regime does not occur, and the momentum dependence of the electron self
energy is less pronounced. Implications for the high-$T_c$ cuprates and for the
use of cluster dynamical mean field methods in wider classes of problems are
discussed.
