  This work proposes a new approach to study transport properties of highly
correlated local structures. The method, dubbed the Logarithmic Discretization
Embedded Cluster Approximation (LDECA), consists of diagonalizing a finite
cluster containing the many-body terms of the Hamiltonian and embedding it into
the rest of the system, combined with Wilson's idea of a logarithmic
discretization of the representation of the Hamiltonian. The physics associated
with both one embedded dot and a double-dot side-coupled to leads is discussed
in detail. In the former case, the results perfectly agree with Bethe ansatz
data, while in the latter, the physics obtained is framed in the conceptual
background of a two-stage Kondo problem. A many-body formalism provides a solid
theoretical foundation to the method. We argue that LDECA is well suited to
study complicated problems such as transport through molecules or quantum dot
structures with complex ground states.
