  A new application of the density matrix renormalization group (DMRG) method
to a system composed of an interacting dot coupled to a infinite one
dimensional lead is presented. This method enables one to study the influence
of the coupling to an external lead on the thermodynamical properties of the
dot. It is shown that this method reproduces known results for a
non-interacting dot coupled to a lead, i.e., that for strong coupling discrete
states remain in the dot. We show that these states are robust and do not
disappear once interactions in the dot are considered. Moreover, due to these
discrete states, Coulomb blockade affects the charging of the dot even though
its strongly coupled to a lead.
