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A new efficient converging perturbation technique valid for arbitrary interaction strength U/t and electron concentration n is applied to study strongly correlated electrons within the repulsive Hubbard model. We test the new perturbation expansion theory in terms of interacting quasi-particles about generalized self-consistent field (GSCF) solution in an entire parameter space. The developed perturbation formalism for strong interaction and large perturbation region differs from the traditional theory on the vicinity of non-interacting electrons by incorporating systematically fluctuations of quasi-particles around self-consistent solution. Performed analytical calculations of the ground state properties in the extreme conditions of one dimensionality provide quite reasonable numerical agreement with the Bethe-ansatz results in the intermediate range of U/t and n. The results are compared with the predictions of traditional perturbation theory. [ABSTRACT FROM AUTHOR]

The shortcomings and advantages of the generalized self-consistent field (GSCF) approach, which includes the electron–hole order parameter [formula] and the average spin s within the one-dimensional repulsive Hubbard model, are analyzed by comparison of the ground state properties with the corresponding Bethe ansatz results in an entire parameter space of interaction strength U/t ≥ 0, magnetic field h ≥ 0 and electron concentration 0 ≤ n ≤ 1. The GSCF spectral characteristics are derived and criteria are found for the stability of incommensurate magnetic phase with the wave number 0 < q < π. The GSCF theory displays a simple relationship for the double occupancy D[sup (+)] in terms of n, s and [formula], where D[sup (+)] underestimates electron correlations at weak and intermediate ranges and overestimates correlations at large interaction strengths. Beyond some critical U/t and n≠1 the GSCF D[sup (+)] for spatially homogeneous state vanishes, while the exact D for all n at h=0 decreases gradually as U/t increases. At n ≠ 1 the GSCF chemical potential μ[sup (+)] overestimates electron correlations everywhere and variation μ[sup (+)] versusn displays electron instability toward the phase separation in the vicinity of n=1. Exactly at n=1 the GSCF μ[sup (+)]versusU/t always underestimates electron correlation and as U/t → ∞ at h=0 we have μ[sup (+)] → 0, while the Bethe ansatz result gives μ → 2t. In the limiting cases U/t → 0 and U/t → ∞ for all h ≥ 0 and 0 ≤ n ≤ 1 the GSCF ground state energy is exact, which is necessary for formulation of converging perturbation procedure about mean field solution in the entire parameter space. [ABSTRACT FROM AUTHOR]

The phase diagram and thermodynamic properties of the Hubbard model in one dimension are calculated numerically within the generalized self-consistent approach over a wide range of temperature T, magnetic field h, interaction strength U/t and electron concentration n. The temperature variation of the transverse magnetization, double occupied sites and chemical potential at various n, U/t and h is also analyzed. The wave vector q for the magnetic order parameter in the vicinity of the half-filling in the metallic phase shows a crossover from incommensurate magnetic phase (0

The accurate analytical and numerical calculations of the electronic band structure and ground state properties of strongly correlated electrons within the Hubbard model are performed by constructing convergent perturbation theory for general interaction strength and electron concentration. We test the developed perturbation approach about mean field solution in the extreme conditions of one dimensionality for entire parameter space of electron interaction U/t and electron concentration n. The many-body perturbation formalism up two second order about the generalized self-consistent field (GSCF) Hamiltonian goes beyond the range of applicability of standard perturbation theory by incorporating systematically the effect of the random-phase-type perturbation techniques and controlled expansion of the energy functional for general U/t and n. The second order perturbation correction vanishes at small and large U/t limit and performed calculations of the ground state energy show a next to the perfect numerical agreement with the Bethe-ansatz results. [ABSTRACT FROM AUTHOR]

One- and two-dimensional attractive Hubbard models in the presence of magnetic field h are studied in a wide range of on-site interaction strength U, temperature T and electron concentration n by means of the generalized self-consistent field (GSCF) approach with renormalized chemical potential. Pairing, the smooth crossover from the BCS regime into the Bose condensation state and the inhomogeneous superconductivity with the non-uniform order parameter are investigated. The excitation spectrum, the momentum distribution function and thermodynamic properties, including the concentration of double occupied sites, the kinetic energy, and the chemical potential, are calculated. The numerical calculations are found in a good agreement with the Bethe-ansatz results and quantum Monte-Carlo calculations in a wide range of system parameters U, n and h. The GSCF theory correctly displays the separation of the energy gap from the order parameter (crossover) as n or U decrease. The concentration of double occupied sites and the bound electron pairs n[sub pair] are calculated and we found a simple relationship between the order parameter and n[sub pair], valid for the arbitrary U and all n in any dimension. The developed GSCF approach in magnetic field suggests a smooth transition into the inhomogeneous superconducting state. [ABSTRACT FROM AUTHOR]

The phase diagram, the Bethe-ansatz ground-state properties, including the chemical potential µ, the spin (magnetic) and charge susceptibilities, are calculated within the one-dimensional Hubbard model in entire range of interaction strength (-∞ < U/t < +∞), magnetic field (h ≥ 0) and all electron concentrations (0 ≤ n ≤ 1). The continuous and smooth variation of µ with n and h in the vicinity of n = 1 points on the gapless character of charge excitations at U < 0 and provides rigorous upper and lower bounds for µ. The spin (magnetic) susceptibility χ at half-filling changes discontinuously as U → 0 and is strongly enhanced by electron repulsion, comparing with that of the non-interacting case. The compressibility κ[sub ch] increases with n at U < 0 and shows non-monotonous behavior with a dramatic increase at U > 0. Variation of κ[sub ch][sup -1] in both repulsive and attractive cases qulitatively well reproduces corresponding behavior of charge stiffness. [ABSTRACT FROM AUTHOR]

The ground-state properties in one-dimensional Hubbard model with on-site attraction and repulsion of electrons in the presence of magnetic field h are calculated by means of the exact Bethe-ansatz formalism and the generalized self-consistent field (GSCF) approach for general electron concentrations n and arbitrary interaction strength. The ground-state properties, including the energy, the average spin (magnetization) and the kinetic energy are compared over a wide range of parameter space. The GSCF theory is in qualitative and in some cases in good quantitative agreement with the exact results. The GSCF theory at U ≤ 0 (or U ≥ 0) differentiates the spin (or charge) energy gap from the BCS (or antiferromagnetic) order parameter and suggests a smooth crossover from the phase with the itinerant BCS-like behavior to the Bose condensation regime of the local pairs. [ABSTRACT FROM AUTHOR]

The exact phase diagram and the ground-state properties of the one-dimensional Hubbard model with arbitrary on-site interaction of electrons are calculated over a wide range of magnetic field and electron concentrations by means of the Bethe-ansatz formalism. The ground-state properties, including the total energy, the average spin (magnetization) and spin (magnetic) susceptibility are investigated for both signs of the interaction strength U/t. The critical behavior near the onset of magnetization and magnetic saturation are also analyzed. At the onset of magnetization and near the magnetic saturation the spin susceptibility χ diverges at all U/t for half-filling case n = 1, whereas for n ≠ 1 it is always finite. The reverse susceptibility χ[sup -1] (U) exhibits anomalous hump, which increases with h or n, and shows discontinuity as U/t → ±0 at infinitesimal h → 0. The analytical results for the ground-state properties in strong and weak interaction limits are in full agreement with our numerical calculations. [ABSTRACT FROM AUTHOR]