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Ferromagnetism in Hubbard Chains

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We analyze the possible occurrence of ferromagnetism in the Hubbard model, by means of an exact diagonalization study performed on 3- to 8-site chains with periodic boundary conditions. In the case of one hole in the half-filled configuration, we find that the Nagaoka state is reached only in the 3- and in the 4-site case. Ground states characterized by unsaturated ferromagnetism are found when the case of more than one hole is considered.
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Superconductivity in Anderson Lattice Model

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We study the superconducting instabilities generated by the inclusion in the Anderson lattice model of a density-density attractive potential between correlated electrons on nearest-neighbouring sites. Using a description of the normal phase based on a perturbative expansion around the atomic limit, we treat the attractive potential in the broken-symmetry Hartree-Fock scheme and analyze which of the possible symmetries of the superconducting order parameter leads to the highest possible transition temperature in the case of a two-dimensional square lattice. For values of the on-site f-repulsion large compared to the hopping amplitude, a suppression of any possible superconducting phase occurs, regardless of the symmetry of the order parameter.
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We analyze the effects of a large spin-orbit coupling on the magnetic state of a d¹ transition-metal ion located in a tetrahedral environment. While in the ideal tetrahedral symmetry the spin-orbit coupling acts only as a perturbation on the atomic energy levels set by the crystal-field splitting, we demonstrate that its effects are strongly enhanced in the case of distorted geometries. In particular, we consider the specific case in which the tetrahedron is compressed along the z direction, and show that, by increasing the degree of flattening, a large spin-orbit interaction (i) can induce a substantial anisotropic, unquenched orbital momentum and (ii) can affect the hierarchy of the lowest energy levels that are involved in the magnetic exchange.
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