Logarithmic discretization in Anderson´s model Is there some motivation for the construction of Ladder operator that compound the recursive halmitonian of the Anderson model for numerical renormalization contained is this paper?
 A: Your question is deep and to the best of my knowledge only partially resolved, see Sec. II of 2007 article in Review of Modern Phsyics. The trick is called  "the Wilson chain" and is essential for NRG to work on strongly correlated models with Kondo-like behavior. 
The Wilson chain construction makes NRG a computationally efficient procedure. My understanding of the intuition behind it is that logarithmic discretization gives you roughly the same resolution after each rescaling step, therefore the diagonalization effort is somehow "balanced" over all relevant energy scales. But as the expert of the field comment in the review quoted above, 

However, this argument in favor of the logarithmic discretization does
  neither explain the need for a mapping to a chain Hamiltonian as in
  Fig. 1c, nor how the problem of an exponentially growing Hilbert space
  with increasing chain length is resolved.

A: Now I know why the Logarithmic discretization are take place in Anderson Model for low temperatures. We want to discretize the energy band-width $[-D,D]$ such that we can perform a numerical calculation. But we want to answering questions of low temperature, and we need to be very careful to apply the thermodynamic limit $N\rightarrow \infty$ before the $T\rightarrow 0$ limit. For understand the dangerous, we can divide the bandwidth, without loss of generality, in $I_n=[\epsilon_n,\epsilon_{n+1}]$ intervals, and then, analyze how this model accommodates this discretization.
The strategy is decompose in Fourier modes the field operator $\phi (\epsilon)$ on $I_n=[\epsilon_n,\epsilon_{n+1}]$. The zeroth mode $p=0$ terms are the mean values of $\phi$ on $I_n$ (discretization), and then, the higer modes $p\neq 0$ represents the correction of the discretize approximation. When we see how the Anderson hamiltonian presents, we see that the impurity only couples to the discretization modes ($p=0$), and the conduction are responsible to the coupling of the discretization modes and the corrections ($p\neq 0$). The ratio of the coupling $p\rightarrow q$ with the usual couplings of the $p=0$ modes take the form of
$$
J_{p,\,q}=\frac{d\epsilon}{\epsilon}|p-q|^{-1}
$$
Then, if we take a linear discretization, in low temperatures, we probe $\epsilon\sim0$ and the continuous are extremely important there ($J_{p,\,q}\rightarrow \infty$). If we take a Logarithm discretization $[\Lambda^{-n},\Lambda^{-n-1}]$, the coupling take the form 
$$
J_{p,\,q}=\frac{1-\Lambda^{-1}}{1+\Lambda^{-1}}|p-q|^{-1}
$$
We may see now that this discretization is give to us a $$J_{p,\,q}\leq\frac{1-\Lambda^{-1}}{1+\Lambda^{-1}}$$ then we can control the discretization by terms of $\Lambda\sim 1$. This natural discretization is property of the conduction band at low temperatures. Of course that some interactions with the conduction band could change the history, but interaction that contains $$
\int _{-D}^{D} \phi(\epsilon)d\epsilon
$$
do not couples the discrete into the continuous corrections.
