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Anomalous Self-Energy Features in the 2D Hubbard Model

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The electronic self-energy of the two-dimensional Hubbard model, computed in the non-crossing approximation within the composite operator method, is studied as a function of frequency as well as temperature at the Fermi surface, for a value of doping at which the pseudogap is already well developed. For values of momentum belonging to the phantom arc of the Fermi surface, both dependences show anomalous power law behavior in contrast to that expected from the Fermi liquid theory.
EN
We study the two-orbital Hubbard model in the limit of vanishing kinetic energy. The phase diagram in the V-J plane, with V and J denoting the interorbital hybridization and exchange coupling respectively, at half filling is obtained. A singlet(dimer)-triplet transition is found for a critical value of the ratio V/J. The entropy of formation, both in the mode and in the particle pictures, presents a jump at the same critical line in conformity with the suggested relation between criticality and entanglement.
EN
By using density matrix renormalization group technique we study the 1D extended anisotropic Heisenberg model. We find that starting from the ferromagnetic phase, the system undergoes two quantum phase transitions induced by frustration. By increasing the next-nearest-neighbor interaction, the ground state of the system changes smoothly from a completely polarized state to a next-nearest-neighbor correlated one. On the contrary, letting the in-plane interaction to be greater than the out-of-plane one, the ground state changes abruptly.
EN
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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