  We present important use cases and limitations when considering results
obtained from Cluster Perturbation Theory (CPT). CPT combines the solutions of
small individual clusters of an infinite lattice system with the Bloch theory
of conventional band theory in order to provide an approximation for the
Green's function in the thermodynamic limit. To this end we are investigating
single-band and multi-band Hubbard models in one- and two-dimensional systems.
A special interest is taken in the supposed pseudo gap regime of the
two-dimensional square lattice at half filling and intermediate interaction
strength ($U \leq 3t$) as well as the metal-insulator transition. We point out
that the finite-size level spacing of the cluster limits the resolution of
spectral features within CPT. This restricts the investigation of asymptotic
properties of the metal-insulator transition, as it would require much larger
cluster sizes that are beyond computational capabilities.
