A multi-orbital iterated perturbation theory for model Hamiltonians and real material-specific calculations of correlated systems

The dynamical mean field theory (DMFT) has emerged as one of the most important frameworks for theoretical investigations of strongly correlated lattice models and real material systems. Within DMFT, a lattice model can be mapped onto the problem of a magnetic impurity embedded in a self-consistently determined bath. The solution of this impurity problem is the most challenging step in this framework. The available numerically exact methods such as quantum Monte Carlo, numerical renormalization group or exact diagonalization are naturally unbiased and accurate, but are computationally expensive. Thus, approximate methods, based e.g. on diagrammatic perturbation theory have gained substantial importance. Although such methods are not always reliable in various parameter regimes such as in the proximity of phase transitions or for strong coupling, 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 such a method, that can be classified as a multi-orbital iterated perturbation theory (MO-IPT) to study N-fold degenerate and non degenerate Anderson impurity models. As applications of the solver, we have embedded the MO-IPT within DMFT and explored 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 (CTQMC). In the case of the single orbital Hubbard model, covalent band insulators and non degenerate multi-orbital Hubbard models, we obtained an excellent agreement between the Matsubara self-energies of MO-IPT and CTQMC. But for the degenerate multi-orbital Hubbard model, we observe that the agreement with CTQMC results gets better as we move away from particle-hole symmetry. We have also integrated MO-IPT+ DMFT 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, SrVO3. A comparison of density of states and photo emission spectrum (PES) with results obtained from different impurity solvers and experiments yields good agreement.