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Exact ground-state properties and phase transitions within one-dimensional Hubbard model in magnetic field

Yang C; Kocharian AN; Chiang YL

Published Jan 1, 2000• 0 citations
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Abstract

[[abstract]]Cited: 0 References: 20 Citation Map Abstract: The phase diagram, the Bethe-ansatz ground-state properties, including the chemical potential mu, the spin (magnetic) and charge susceptibilities, are calculated within the one-dimensional Hubbard model in entire range of interaction strength (-infinity < U/t < + infinity), magnetic field (h greater than or equal to 0) and all electron concentrations (0 less than or equal to n less than or equal to 1). The continuous and smooth variation of mu 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 <mu>. The spin (magnetic) susceptibility chi 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 rc,h increases with n at U < 0 and shows non-monotonous behavior with a dramatic increase at U > 0. Variation of k(ch)(-1) in both repulsive and attractive cases qulitatively well reproduces corresponding behavior of charge stiffness.

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Exact Ground-State Properties and Phase Transitions within One-dimensional Hubbard Model in Magnetic Field

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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) susceptability χ at half-filling changes discontinuously as U→0 and is strongly enhanced by electron repulsion, comparing with that of the non-interactig case. The compressibility κ ch increases with n at U<0 and shows non-monotonous behavior with a dramatic increase at U>0. Variations of κ ch -1 in both repulsive and attractive cases qualitatively well reproduces corresponding behavior of charge stiffness.

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International Journal of Modern Physics B•Dec 20, 1999•4 citations
[[abstract]]Cited: 0 References: 20 Citation Map Abstract: The phase diagram, the Bethe-ansatz ground-state properties, including the chemical potential mu, the spin (magnetic) and charge susceptibilities, are calculated within the one-dimensional Hubbard model in entire range of interaction strength (-infinity < U/t < + infinity), magnetic field (h greater than or equal to 0) and all electron concentrations (0 less than or equal to n less than or equal to 1). The continuous and smooth variation of mu 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 <mu>. The spin (magnetic) susceptibility chi 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 rc,h increases with n at U < 0 and shows non-monotonous behavior with a dramatic increase at U > 0. Variation of k(ch)(-1) in both repulsive and attractive cases qulitatively well reproduces corresponding behavior of charge stiffness.
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) susceptability χ at half-filling changes discontinuously as U→0 and is strongly enhanced by electron repulsion, comparing with that of the non-interactig case. The compressibility κ ch increases with n at U<0 and shows non-monotonous behavior with a dramatic increase at U>0. Variations of κ ch -1 in both repulsive and attractive cases qualitatively well reproduces corresponding behavior of charge stiffness.
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.
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-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]]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 < q < pi) into the state with strong antiferromagnetic correlations (q = pi) as temperature is increased. Overall our numerical results in the approximate theory at finite temperatures are in good quantitative and qualitative agreement with the Bethe-ansatz results.
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.