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Journal of the Physical Society of Japan

Phase Diagram and Magnetic Correlations in One-Dimensional Repulsive Hubbard Model with Magnetic Field

Chi Yang, ARMEN N. KOCHARIAN, Y. L. Chiang, Tin-Yu Chou

Published Jan 1, 2002• 0 citations
Publisher

Abstract

The generalized self-consistent field (GSCF) theory for the one-dimensional repulsive Hubbard model at half-filling is examined in the presence of magnetic field h in wide range of interaction strength U / t . The evolution of the energy gap in the presence of magnetc field describes a magnetic crossover from itinerant magnetism of weakly bound electron-hole pairs with k F =π/2 to the localized magnetic regime, with the Bose condensation of local electron-hole pairs ( k F =0).

DOI
10.1143/jpsjs.71s.193

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Journal of Physics Condensed Matter•Aug 2, 2000•24 citations
The generalized self-consistent field (GSCF) theory for the one-dimensional repulsive Hubbard model at half-filling is examined in the presence of magnetic field h in wide range of interaction strength U / t . The evolution of the energy gap in the presence of magnetc field describes a magnetic crossover from itinerant magnetism of weakly bound electron-hole pairs with k F =π/2 to the localized magnetic regime, with the Bose condensation of local electron-hole pairs ( k F =0).
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.
The ground-state (GS) properties of the one-dimensional (1D) Hubbard model at half-filling are examined in the presence of a magnetic field using the generalized mean-field (GMF) approach, which includes the spin-density and the electron-hole correlations on an equal footing. The GMF formalism provides insight into both the metal-insulator transition and the transition from itinerant to localized magnetism with applied field. The GMF theory can differentiate the energy gap from the antiferromagnetic order parameter in the presence of a magnetic field. The numerical results for the GS energy, the magnetization, the spin susceptibility, and the number of doubly occupied sites are in good agreement with the exact results over a wide range of U / t and h / t . The calculated h - U phase diagram exhibits a magnetic crossover from itinerant electron-hole pairs to a Bose-Einstein condensate state of local pairs. The overall picture of the magnetic crossover in 1D is found to be similar for the simple case of constant density of states, putting the GMF approach on a firmer basis in two and three dimensions.
[[abstract]]The ground-state energy, the concentration of double occupied sites and the density of bound electron pairs in low-dimensional attractive Hubbard model are calculated by means of the generalized self-consistent field (GSCF) approach. This approach gives an excellent agreement with the corresponding Bethe-ansatz solution and the quantum Monte-Carlo calculations in a wide range of interaction strength U < 0 and electron concentration n. A simple relationship is found between the order parameter and the density of bound electron pairs, valid for any dimension and in entire parameter space U, n and magnetic field h. The electron pairing and the crossover from the itinerant BCS regime into the Bose condensation regime of local pairs are studied in dependence of both U and n. The GSCF theory correctly displays the separation of the energy gap from the BCS order parameter at n not equal 1 as \U \ increases. (C) 2001 Elsevier Science B.V. All rights reserved.
The shortcomings and advantages of the generalized self-consistent field (GSCF) approach, which includes the electron–hole order parameter [Formula: see text] 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(+) in terms of n, s and [Formula: see text], where D(+) 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(+) 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(+) overestimates electron correlations everywhere and variation μ(+)versusn displays electron instability toward the phase separation in the vicinity of n=1. Exactly at n=1 the GSCF μ(+)versusU/t always underestimates electron correlation and as U/t → ∞ at h=0 we have μ(+) → 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.
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 pair are calculated and we found a simple relationship between the order parameter and n 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.
The exact phase diagrams of the one-dimensional Hubbard model, both attractive and repulsive, in the presence of an arbitrary magnetic field h for various electron concentrations n and on-site interaction strengths U <0 or U >0 are calculated and investigated. The exact ground-state properties, namely, the ground-state energy, the average spin (magnetization), the concentration of the doubly occupied sites, the kinetic energy, the chemical potential, the spin (magnetic) susceptibility and the charge compressibility, are calculated and examined over a wide range of interaction strengths U for various h and n . It is found that the spin susceptibility at half-filling is non-analytic and changes discontinuously as U →0. The exact theory shows the absence of a charge energy gap in the U ⩽0 region for all n and provides, for the chemical potential, the rigorous upper and lower bounds for half-filled and empty bands respectively. The analytical results derived for the weak-coupling limit and asymptotic expansions for strong coupling are in full agreement with the numerical calculations.