  The one-dimensional Hubbard model is investigated by means of two different
cluster schemes suited to introduce short-range spatial correlations beyond the
single-site Dynamical Mean-Field Theory, namely the Cluster-Dynamical
Mean-Field Theory and its periodized version. It is shown that both cluster
schemes are able to describe with extreme accuracy the evolution of the density
as a function of the chemical potential from the Mott insulator to the metallic
state. Using exact diagonalization to solve the cluster impurity model, we
discuss the role of the truncation of the Hilbert space of the bath, and
propose an algorithm that gives higher weights to the low frequency
hybridization matrix elements and improves the speed of the convergence of the
algorithm.
