Abstract:
We study with exact diagonalization the zero temperature properties of the quarter-filled extended Hubbard model on a square lattice. We find that increasing the ratio of the intersite Coulomb repulsion, $V$, to the band width drives the system from a metal to a charge ordered insulator. The evolution of the optical conductivity spectrum with increasing $V$ is compared to the observed optical conductivity of several layered molecular crystals with the theta and beta'' crystal structures.

Abstract:
We have studied the stability of the ferromagnetic state in the infinite-U Hubbard model on a square lattice by approximate diagonalization of finite lattices using the density matrix renormalization group technique. By studying lattices with up to 5X20 sites, we have found the ferromagnetic state to be stable below the hole density of 22 percent. Beyond 22 percent of hole doping, the total spin of the ground state decreased gradually to zero with increasing hole density.

Abstract:
The zero temperature transition from a paramagnetic metal to a paramagnetic insulator is investigated in the Dynamical Mean Field Theory for the Hubbard model. The self-energy of the effective impurity Anderson model (on which the Hubbard model is mapped) is calculated using Wilson's Numerical Renormalization Group method. Results for quasiparticle weight, spectral function and self-energy are discussed for Bethe and hypercubic lattice. In both cases, the metal-insulator transition is found to occur via the vanishing of a quasiparticle resonance which appears to be isolated from the Hubbard bands.

Abstract:
We investigate the two-dimensional Hubbard model on the triangular lattice with anisotropic hopping integrals at half filling. By means of a self-energy functional approach, we discuss how stable the non-magnetic state is against magnetically ordered states in the system. We present the zero-temperature phase diagram, where the normal metallic state competes with magnetically ordered states with $(\pi, \pi)$ and $(2\pi/3, 2\pi/3)$ structures. It is shown that a non-magnetic Mott insulating state is not realized as the ground state, in the present framework, but as a meta-stable state near the magnetically ordered phase with $(2\pi/3, 2\pi/3)$ structure.

Abstract:
We have studied finite-sized single band Hubbard chains with Fibonacci modulation for half filling within a mean field approximation. The ground state properties, together with the dc conductivity both at zero and non-zero temperatures, are calculated for such quasi-periodic Hubbard chains. While a reduction in the conductivity is found for strong electronic interaction or strong Fibonacci modulation, a competition between these two is observed to enhance the conductivity. The results at finite temperatures also illustrate some interesting features of such finite-sized systems.

Abstract:
We study the effect of strong correlations on the zero bias anomaly (ZBA) in disordered interacting systems. We focus on the two-dimensional extended Anderson-Hubbard model, which has both on-site and nearest-neighbor interactions on a square lattice. We use a variation of dynamical mean field theory in which the diagonal self-energy is solved self-consistently at each site on the lattice for each realization of the randomly-distributed disorder potential. Since the ZBA occurs in systems with both strong disorder and strong interactions, we use a simplified atomic-limit approximation for the diagonal inelastic self-energy that becomes exact in the large-disorder limit. The off-diagonal self-energy is treated within the Hartree-Fock approximation. The validity of these approximations is discussed in detail. We find that strong correlations have a significant effect on the ZBA at half filling, and enhance the Coulomb gap when the interaction is finite-ranged.

Abstract:
We apply the density matrix renormalization group (DMRG) to study the phase diagram of the infinite U Hubbard model on 2-, 4-, and 6-leg ladders. Where the results are largely insensitive to the ladder width, we consider the results representative of the 2D square lattice model. We find a fully polarized ferromagnetic Fermi liquid phase when n, the density of electrons per site, is in the range 1>n>n_F ~ 4/5. For n=3/4 we find an unexpected commensurate insulating "checkerboard" phase with coexisting bond density order with 4 sites per unit cell and block spin antiferromagnetic order with 8 sites per unit cell. For 3/4 > n, the wider ladders have unpolarized groundstates, which is suggestive that the same is true in 2D.

Abstract:
We study the Hubbard model on a hypercubic lattice with regard to the possibility of itinerant ferromagnetism. The Dynamical Mean Field theory is used to map the lattice model on an effective local problem, which is treated with help of the Non Crossing Approximation. By investigating spin dependent one-particle Green's functions and the magnetic susceptibility, a region with nonvanishing ferromagnetic polarization is found in the limit $U\to\infty$. The $\delta$-T-phase diagram as well as thermodynamic quantities are discussed. The dependence of the Curie temperature on the Coulomb interaction and the competition between ferromagnetism and antiferromagnetism are studied in the large $U$ limit of the Hubbard model.

Abstract:
By the spin-fermion formula, the Hubbard model on the honeycomb lattice is represented by a U(2) gauge theory in the mean field method, non-Abelian vortex solutions are constructed based on this theory. The quantization condition shows that the magnetic flux quanta are half-integer. There are $2k$ bosonic zero modes for $k$ winding vortices. For the fermions, there are 2 zero energy states (ZESs) corresponding to the single elementary vortex. In the vortex core and on the edge, the system are in the semi-metal phase with a spin gap and in the insulator phase with N\'eel order phase, and can be mapped to the superconductor in class A and CI, respectively.

Abstract:
The infinite U Hubbard model, with exclusion of double occupancy of sites, can be considered as a free orthofermion Hamiltonian which is exactly soluble. It is found that the orthofermion distribution function is similar to the mean number of trapped electrons in an impurity in a semiconductor where the double occupancy of the impurity is forbidden and similar to the distribution function of the usual fermions. In one dimension, the thermodynamics of free orthofermions gives the known exact results of the infinite U Hubbard model. Thus it shows that at least in one dimension the fermions with exclusion of double occupancy of sites behave as free orthofermions. Since free orthofermions Hamiltonian is exactly soluble in any dimension, it can be employed to ascertain the accuracy of the approximate solutions of the Hubbard model, frequently used for the strongly correlated electron systems like high temperature superconductors.