Spectral Function Calculation for Strongly Correlating Systems

This thesis presents an efficient approach to calculate dynamical properties of solids with strong electron correlations. The fast cluster method, a socalled finite temperature Lanczos method is combined with the Dynamical mean-field theory (DMFT) in order to study orbital degenerate systems as function of temperature. The full local Coulomb interaction was taken into account in all calculations. A first application is two test systems: 5 + 1 and 5 + 5 Anderson impurity models. In the case of 5 + 1 Anderson impurity model it is possible to take into account a large number of eigenstates: Narnoldi > 100. The chemical potential of the system μ were changed in a broad range which leads to a change of a multiplet structure of the spectrum. In all this range of chemical potential μ the ground state of the system is degenerate. At zero temperature it were found that the temperature Lanczos calculations reproduce the correct density of states obtained with exact diagonalization if one chooses the set of ground states which remains the symmetry of the system. If all degenerate ground states are taken into account than the temperature Lanczos method reproduces the correct density of states of the test systems with a good accuracy. In the case of finite temperaure calculations electron transitions to higher energy levels become important. Therefore calculations with Narnoldi = 1 do not reproduce the DOS obtained with exact diagonalitation at any parameters. One needs to consider not only the ground state but also low-energy excited states. In the second part of the thesis the problem known as double-counting one for systems with strong electron correlations is considered. We conducted an extensive study of the charge transfer system NiO in the LDA+DMFT framework using quantum Monte Carlo and temperature Lanczos impurity solvers. By treating the double-counting correction as an adjustable parameter we systematically investigated the effects of different choices for the double counting on the spectral function. Different methods for fixing the double counting correction can drive the result from Mott insulating to al-