  The numerical renormalization group method is used to investigate zero
temperature phase transitions in quantum impurity systems, in particular in the
soft-gap Anderson model, where an impurity couples to a non-trivial fermionic
bath. In this case, zero temperature phase transitions occur between two
different phases whose fixed points can be built up of non-interacting
single-particle states. However, the quantum critical point cannot be described
by non-interacting fermionic or bosonic excitations.
