  Perturbative schemes utilizing a spectral moment expansion are well known and
extensively used for investigating the physics of model Hamiltonians and real
material systems. The advantages they offer, in terms of being computationally
inexpensive, with real frequency output at zero and finite temperatures,
compensate for their deficiencies and offer a quick, qualitative analysis of
the system behavior. In this work, we have developed a method, that can be
classified as a multi-orbital iterative perturbation theory (MO-IPT) to study
N-fold degenerate and non degenerate Anderson impurity models. As applications
of the solver, we have combined the method with dynamical mean field theory to
explore lattice models like the single orbital Hubbard model, covalent band
insulator and the multi-orbital Hubbard model for density-density type
interactions in different parameter regimes. The Hund's coupling effects in
case of multiple orbitals is also studied. The limitations and quality of
results are gauged through extensive comparison with data from the numerically
exact continuous time quantum Monte Carlo method (hybridization expansion
CTQMC). In general we observe that the agreement with CTQMC results gets better
as we move away from particle-hole symmetry. We have integrated MO-IPT with
density functional theory based electronic structure methods to study real
material systems. As a test case, we have studied the classic, strongly
correlated electronic material, SrVO$_3$. A comparison of density of states and
photo emission spectrum (PES) with results obtained from different impurity
solvers and experiments yields good agreement.
