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The dynamical mean field theory (DMFT) has become a standard technique forthe study of strongly correlated models and materials overcoming some of thelimitations of density functional approaches based on local approximations. Animportant step in this method involves the calculation of response functions ofa multiorbital impurity problem which is related to the original model.Recently there has been considerable progress in the development of techniquesbased on the density matrix renormalization group (DMRG) and related matrixproduct states (MPS) implying a substantial improvement to previous methods. Inthis article we review some of the standard algorithms and compare them to thenewly developed techniques, showing examples for the particular case of thehalf-filled two-band Hubbard model.

State-of-the-art techniques for calculating spectral functions in models for correlated materials