Generalized numerical renormalization group for dynamical quantities

In this paper we introduce a new approach for calculating dynamical propert ies within the numerical renormalization group. It is demonstrated that the method previously used fails for the Anderson impurity in a magnetic field due to the absence of energy scale separation. The problem is solved by ev aluating the Green function with respect to the reduced density matrix of t he frill system, leading to accurate spectra in agreement with the static m agnetization. The new procedure provides a unifying framework for calculati ng dynamics at any temperature and represents the correct extension of Wils on's original thermodynamic calculation.