such as Heisenberg, Hubbard, etc ... The [*key difference*]{} is that in the Kondo model there exists a [*recursion relation*]{} for Hamiltonians at each step of the RG-elimination of degrees of freedom. The existence of such recursion relation facilitates enormously the work, but as it happens it is specific of [*impurity problems*]{}.

From the numerical point of view, the Block Renormalization Group procedure proved to be not fully reliable in the past particularly in comparison with other numerical approaches, such as the Quantum MonteCarlo method which were being developed at the same time. This was one of the reasons why the BRG methods remained undeveloped during the ’80’s until the begining of the ’90’s when they are making a comeback as one of the most powerful numerical tools when dealing with zero temperature properties of many-body systems.

Let us first summarize the main features of the real-space RG. The problem that one faces generically is that of diagonalizing a quantum lattice Hamiltonian $H$, i.e.,

$$H |\psi > = E |\psi >
\label{1}$$

where $|\psi >$ is a state in the Hilbert space ${\cal H}$. If the lattice has N sites and there are $k$ possible states per site then the 