  We propose to calculate spectral functions of quantum impurity models using
the Time Evolving Block Decimation (TEBD) for Matrix Product States. The
resolution of the spectral function is improved by a so-called linear
prediction approach. We apply the method as an impurity solver within the
Dynamical Mean Field Theory (DMFT) for the single- and two-band Hubbard model
on the Bethe lattice. For the single-band model we observe sharp features at
the inner edges of the Hubbard bands. A finite size scaling shows that they
remain present in the thermodynamic limit. We analyze the real time-dependence
of the double occupation after adding a single electron and observe
oscillations at the same energy as the sharp feature in the Hubbard band,
indicating a long-lived coherent superposition of states that correspond to the
Kondo peak and the side peaks. For a two-band Hubbard model we observe an even
richer structure in the Hubbard bands, which cannot be related to a multiplet
structure of the impurity, in addition to sharp excitations at the band edges
of a type similar to the single-band case.
