  Recently solvers for the Anderson impurity model (AIM) working directly on
the real-frequency axis have gained much interest. A simple and yet frequently
used impurity solver is exact diagonalization (ED), which is based on a
discretization of the AIM bath degrees of freedom. Usually, the bath parameters
cannot be obtained directly on the real-frequency axis, but have to be
determined by a fit procedure on the Matsubara axis. In this work we present an
approach where the bath degrees of freedom are first discretized directly on
the real-frequency axis using a large number of bath sites ($\approx 50$).
Then, the bath is optimized by unitary transformations such that it separates
into two parts that are weakly coupled. One part contains the impurity site and
its interacting Green's functions can be determined with ED. The other (larger)
part is a non-interacting system containing all the remaining bath sites.
Finally, the Green's function of the full AIM is calculated via coupling these
two parts with cluster perturbation theory.
