  We present an efficient exact diagonalization scheme for the extended
dynamical mean-field theory and apply it to the extended Hubbard model on the
square lattice with nonlocal charge-charge interactions. Our solver reproduces
the phase diagram of this approximation with good accuracy. Details on the
numerical treatment of the large Hilbert space of the auxiliary
Holstein-Anderson impurity problem are provided. Benchmarks with a numerically
exact strong-coupling continuous-time quantum-Monte Carlo solver show better
convergence behavior of the exact diagonalization in the deep insulator.
Special attention is given to possible effects due to the discretization of the
bosonic bath. We discuss the quality of real axis spectra and address the
question of screening in the Mott insulator within extended dynamical
mean-field theory.
