We study the multiband mechanism to favour a ferromagnetic insulating ground state within a two-band Hubbard model. Besides perturbation theory we use exact diagonalization studies to examine the ground state of chains and 2D-lattices. According to second order perturbation theory the exact diagonalization yields a fully polarized ferromagnetic ground state, if the hopping between two ground state orbitals of neighbouring atoms t_{gg} is small and the hopping between a ground state orbital and an excited orbital t_{ge} dominates. However, in contrast to the suggestion from the second order perturbation theory this ferromagnetic state is stable only for very small hopping integrals U≫ t_{ge}>t_{gg}. For larger t _{ge} quantum interference effects lead to complex magnetic structures.
In this paper we report on some ground-state properties of the spin-1/2 Heisenberg antiferromagnet on the two-dimensional square-kagomé lattice. Finite N-spin systems were investigated with the use of the resonating valence bond method. Like in the case of spin system on kagomé lattice we find the almost flat dependence of mean singlet length on 1/N.
Based on the triangular lattice and its depletions there are three simple frustrated antiferromagnetic Heisenberg models in two dimensions. The first two, the triangular and kagomé lattices, have been examined in the recent past. The triangular lattice seems to have a long range order whereas the kagomé does not show the long range order. But these results are still controversial. This work is concentrated on a third type of this lattice family in order to improve the understanding of the connection between the long range order and coordination number in low dimensional systems. Bets has described the geometric properties of this lattice. It has a coordination number 5, which lies precisely between coordination numbers 6 and 4 of the other two lattices. The low-lying spectra and the correlation functions of finite lattices have been examined to discuss the possibility of a long range ordered ground state in the 1/7-depleted triangular lattice. The low-lying spectrum is generated by an exact diagonalization, and the tower of states behavior points to a long range ordered ground state.
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