The Hubbard model in the two-pole approximation

The two-dimensional Hubbard model is analyzed in the framework of the two-pole expansion. It is demonstrated that several theoretical approaches, when considered at their lowest level, are all equivalent and share the property of satisfying the conservation of the first four spectral momenta. It emerges that the various methods differ only in the way of fixing the internal parameters and that it exists a unique way to preserve simultaneously the Pauli principle and the particle-hole symmetry. A comprehensive comparison with respect to some general symmetry properties and the data from quantum Monte Carlo analysis shows the relevance of imposing the Pauli principle.Comment: 12 pages, 8 embedded Postscript figures, RevTeX, submitted to Int. Jou. Mod. Phys.

Anisotropic superexchange of a 90 degree Cu-O-Cu bond

The magnetic anisotropy af a rectangular Cu-O-Cu bond is investigated in second order of the spin-orbit interaction. Such a bond is characteristic for cuprates having edge sharing CuO_2 chains, and exists also in the Cu_3O_4 plane or in ladder compounds. For a ferromagnetic coupling between the copper spins an easy axis is found perpendicular to the copper oxygen plaquettes in agreement with the experimental spin structure of Li_2CuO_2. In addition, a pseudo-dipolar interaction is derived. Its estimation in the case of the Cu_3O_4 plane (which is present for instance in Ba_2Cu_3O_4Cl_2 or Sr_2Cu_3O_4Cl_2) gives a value which is however two orders of magnitude smaller than the usual dipole-dipole interaction.Comment: 6 pages, 2 figures, improved referenc

Normal Fermi Liquid Behavior of Quasiholes in the Spin-Polaron Model for Copper Oxides

Based on the t-J model and the self-consistent Born approximation, the damping of quasiparticle hole states near the Fermi surface is calculated in a low doping regime. Renormalization of spin-wave excitations due to hole doping is taken into account. The damping is shown to be described by a familiar form $\text{Im}\Sigma({\bf k}^{\prime},\epsilon)\propto (\epsilon^{2}/ \epsilon_{F})\ln(\epsilon/ \epsilon_{F})$ characteristic of the 2-dimensional Fermi liquid, in contrast with the earlier statement reported by Li and Gong [Phys. Rev. B {\bf 51}, 6343 (1995)] on the marginal Fermi liquid behavior of quasiholes

Angle resolved photoemission spectroscopy of Sr_2CuO_2Cl_2 - a revisit

We have investigated the lowest binding-energy electronic structure of the model cuprate Sr_2CuO_2Cl_2 using angle resolved photoemission spectroscopy (ARPES). Our data from about 80 cleavages of Sr_2CuO_2Cl_2 single crystals give a comprehensive, self-consistent picture of the nature of the first electron-removal state in this model undoped CuO_2-plane cuprate. Firstly, we show a strong dependence on the polarization of the excitation light which is understandable in the context of the matrix element governing the photoemission process, which gives a state with the symmetry of a Zhang-Rice singlet. Secondly, the strong, oscillatory dependence of the intensity of the Zhang-Rice singlet on the exciting photon-energy is shown to be consistent with interference effects connected with the periodicity of the crystal structure in the crystallographic c-direction. Thirdly, we measured the dispersion of the first electron-removal states along G->(pi,pi) and G->(pi,0), the latter being controversial in the literature, and have shown that the data are best fitted using an extended t-J-model, and extract the relevant model parameters. An analysis of the spectral weight of the first ionization states for different excitation energies within the approach used by Leung et al. (Phys. Rev. B56, 6320 (1997)) results in a strongly photon-energy dependent ratio between the coherent and incoherent spectral weight. The possible reasons for this observation and its physical implications are discussed.Comment: 10 pages, 8 figure

The Hubbard model within the equations of motion approach

The Hubbard model has a special role in Condensed Matter Theory as it is considered as the simplest Hamiltonian model one can write in order to describe anomalous physical properties of some class of real materials. Unfortunately, this model is not exactly solved except for some limits and therefore one should resort to analytical methods, like the Equations of Motion Approach, or to numerical techniques in order to attain a description of its relevant features in the whole range of physical parameters (interaction, filling and temperature). In this manuscript, the Composite Operator Method, which exploits the above mentioned analytical technique, is presented and systematically applied in order to get information about the behavior of all relevant properties of the model (local, thermodynamic, single- and two- particle ones) in comparison with many other analytical techniques, the above cited known limits and numerical simulations. Within this approach, the Hubbard model is shown to be also capable to describe some anomalous behaviors of the cuprate superconductors.Comment: 232 pages, more than 300 figures, more than 500 reference