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In this Master's thesis, the Kondo-lattice model with quantum localized spins on the triangular lattice is to be investigated. The method to be used is the variational cluster approach (VCA). Questions to be discussed here include the stability of non-coplanar magnetic order and triplet superconductivity. Moreover, the impact of quantum fluctuations can be studied.

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In this Master's thesis, non-equilibrium processes should be simulated on the triangular lattice in two dimensions. The aim is to find equilibrium phases and identify non-equilibrium states.

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In this Master's thesis,the spectral density for one charge carrier in t-J models is to be studied using cluster-perturbation theory, where the description of the antiferromagnetic background is to be reformulated from spins into bosons.

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In this Master's Thesis, the Kugel-Khomskii model for one electron should be studied on the honeycomb lattice for increasing spin-orbit coupling strength and varying Hund's rule coupling. To this effect, the Hamiltonian has to be extended and analyzed by exact diagonalization methods.

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