We discuss the magnetic phases of the Hubbard model for the honeycomb lattice both in two and three spatial dimensions. A ground state phase diagram is obtained depending on the interaction strength U and electronic density n. We find a first order phase transition between ferromagnetic regions where the spin is maximally polarized (Nagaoka ferromagnetism) and regions with smaller magnetization (weak ferromagnetism). When taking into account the possibility of spiral states, we find that the lowest critical U is obtained for an ordering momentum different from zero. The evolution of the ordering momentum with doping is discussed. The magnetic excitations (spin waves) in the antiferromagnetic insulating phase are calculated from the random-phase approximation for the spin susceptibility. We also compute the spin fluctuation correction to the mean field magnetization by virtual emission/absorption of spin waves. In the large U limit, the renormalized magnetization agrees qualitatively with the Holstein-Primakoff theory of the Heisenberg antiferromagnet, although the latter approach produces a larger renormalization.

We calculate the antiferromagnetic spin-wave dispersion in a half-filled Hubbard model for a two-dimensional square lattice, and find it to be in excellent agreement with recent high-resolution inelastic neutron scattering performed on La2CuO4 [Phys. Rev. Lett. 86, 5377 (2001)].PACS numbers: 75.30. Ds, 71.10.Fd, 75.40.Gb After over a decade of intense research on the microscopic origin of high-temperature superconductivity in cuprates, there is no general consensus on the microscopic Hamiltonian suitable for describing these materials. Nevertheless, it appears that magnetic fluctuations must play an important role. Therefore, the study of magnetic fluctuations in the high-temperature superconductor parent compounds, such as La 2 CuO 4 , is an important field of research, both theoretical and experimental.In two recent papers, 1,2 high-resolution inelastic neutron-scattering measurements were performed on two different two-dimensional spin-1/2 quantum antiferromagnets. These are copper deuteroformate tetradeuterate (CFTD) and La 2 CuO 4 . Surprisingly, the dispersion at the zone boundary observed in the two materials, does not agree with spin-wave theory predictions. 3 Moreover the amount of dispersion is not the same for both materials. In CFTD the dispersion is about 6% from ω(π/2, π/2) to ω(π, 0), whereas in La 2 CuO 4 it is about -13% along the same direction. In the case of CFTD the dispersion at the zone boundary can be explained using the nearest-neighbor Heisenberg model alone, 2 and highprecision quantum Monte Carlo simulations have confirmed that this is so. 4 On the other hand, an explanation for the observed dispersion in La 2 CuO 4 was proposed, 1 using an extended Heisenberg model 5,6 involving first-, second-, and third-nearest-neighbor interactions as well as interactions among four spins. This extended model was obtained from the Hubbard model, using perturbation theory, and is diagonalized afterward using classical (large-S) linear spin-wave theory. 1 The La 2 CuO 4 results clearly show that the usual Heisenberg model is insufficient to explain the experimental data, and that the Hubbard model is the correct Hamiltonian for describing the magnetic interactions in the cuprates. 7 In this work we do not use perturbation theory for deriving an effective magnetic Hamiltonian. Instead we work directly with the Hubbard model. We consider a half-filled Hubbard model in a spin-densitywave (SDW)-broken symmetry ground state and, by summing up all ladder diagrams, we compute the transverse spin susceptibility and from this obtain the spinwave dispersion.The Hubbard model for a square lattice of N sites is defined as

The problem of Andreev reflection between a normal metal and a multiband superconductor is addressed. The appropriate matching conditions for the wave function at the interface are established on the basis of an extension of quantum waveguide theory to these systems. Interference effects between different bands of the superconductor manifest themselves in the conductance and the case of FeAs superconductors is specifically considered, in the framework of a recently proposed effective two-band model, in the sign-reversed s-wave pairing scenario. Resonant transmission through surface Andreev bound states is found as well as destructive interference effects that produce zeros in the conductance at normal incidence. Both these effects occur at nonzero bias voltage.