Alternative discretization in the numerical renormalization-group method

A logarithmic discretization procedure, alternative to the one traditionally employed in the Numerical renormalization-group computations of physical properties for impurity models, is introduced. While the traditional method neglects the coupling of the conduction states most localized around the impurity site to all other conduction states, this one constructs a nonorthogonal basis that diagonalizes the conduction-band Hamiltonian and neglects the overlap between basis states. Unlike the traditional procedure, which underestimates the spectral density of the coupling between the conduction band and the impurity, this one requires no ad hoc renormalization of coupling constants. Numerical examples covering the specific heat for the Kondo model and the impurity spectral densities for the uncorrelated Anderson model show that, for the same discretization parameters, this procedure is substantially more accurate than the traditional one.