An exact-diagonalization technique on small clusters is used to study the ground states and single-particle excitations of the Hubbard model with on-site (U) and nearest-neighbor (V) Coulombic repulsive interactions. It is shown that the long-range charge-density-wave state realized in a half-filled two-dimensional square lattice for 4V\ensuremath{\gtrsim}U persists up to quarter filling, and that the doped carriers form a small Fermi surface that encloses an area corresponding to the number of doped carriers rather than the total number of electrons involved in the system. The present result offers a well-defined counterexample in the discussion of the Fermi-surface dimensions of strongly correlated electron systems, and may provide a complementary understanding of the large Fermi surface believed to exist in the ordinary Hubbard model.
Monte Carlo simulations are used to study the charge-density-wave to spin-density-wave transition in the one-dimensional Hubbard model with on-site (
U) and nearest-neighbor (
V) repulsion. The transition is found to be continuous for small
U and first order for large
U, with the crossover occurring around $U\ensuremath{\sim}3$. The transition line deviates somewhat from the theoretical prediction
U=2V towards the charge-density-wave phase for intermediate coupling. A qualitative explanation for the results is given by use of strong-coupling arguments.
This thesis examines the properties of a new microscopic model for non-Fermi-liquid behavior and d-wave pairing in a strongly correlated quasi-two-dimensional (2D) electron gas with purely repulsive interactions. Themicroscopic Hamiltonian for this system involves a nearest neighbor electron hopping matrix element t, an on-site Coulom b repulsion U , and a nearest neighbor Coulomb repulsion V. We suggest that nearest neighbor Coulomb repulsion on the energy scale of t stabilizes a state in which electrons undergo a �somersault� in their internal spin-space (spin-flux). Spin-flux is a new form of spontaneous symmetry breaking in a strongly correlated electron system in which the Hamiltonian acquires a term with the symmetry of spin-orbit coupling at the mean-field level. Spin-flux modifies the single quasi-particle dispersion relations from that of a conventional antiferro-magnet (AFM ). When this spin-1/2 A FM insulator is doped, the charge carriers are mobile, charged, bosonic meron-vortex solitons accompanied by unoccupied states deep inside the Mott-Hubbard charge-transfer gap. This model provides a unified microscopic basis for (i) non-Fermi-liquid transport properties for low and intermediate doping, (ii) mid-infrared optical absorption, (iii) destruction of A FM long range order with doping, (iv) angled resolved spectroscopy (ARPES), (v) d-wave preformed charge carrier pairs, an d (vi) a transition from the non-Fermi liquid state to a conventional Fermi-liquid metal for large doping. The approximations used to study the 2D spin-flux Hubbard model are the unrestricted Hartree-Fock Approximation and the Configuration Interaction (C l) Method. In ID, the C l approximation leads to excellent agreement with the exact Bethe Ansatz solution of the Hubbard model, as well as a clear demonstration of the spin-charge separation: the charge of the doping hole is carried by charged bosonic domain-walls, while the spin of the doping hole is carried by neutral fermionic domain-walls. In 2D, the C l method suggests a precursor to the spin-charge separation: addition of a single hole leads to the appearance of a charge-carrying vortex (the meron-vortex) bound to a spin-carrying antivortex.