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Pairing, crossover and inhomogeneous superconductivity in the attractive Hubbard model

Kocharian AN; Yang C; Chiang YL

Published Jan 1, 2000• 0 citations
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Abstract

[[abstract]]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 ail n in any dimension. The developed GSCF approach in magnetic field suggests a smooth transition into the inhomogeneous superconducting state.

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[[abstract]]Thermodynamic characteristics of the one-dimensional attractive Hubbard model are calculated by means of the generalized self-consistent field (GSCF) approach for a wide range of interaction strength U less than or equal to, 0, in the presence of external magnetic field h greater than or equal to 0, temperature T greater than or equal to 0 and electron concentration 0 less than or equal to n less than or equal to 1. The GSCF theory shows a sharp transition driven by h > 0 and T from the uniform superconducting state into a spatially inhomogeneous state in which the order parameter Delta ((-))(q) has wave vector (0 < \q \ less than or equal to pi). The concentration of double occupied sites and the bound electron pairs with opposite spins n(pair) are calculated and we found a simple relationship between the order parameters Delta ((-))(q) and average spin s, valid for the arbitrary U, all n and h. (C) 2001 Published by Elsevier Science B.V.

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The phase diagram and inhomogenous superconductivity in the one-dimensional attractive Hubbard model

Kocharian AN; Yang C; Chiang YL

[[abstract]]The thermodynamic phase diagram of the attractive Hubbard model in the presence of magnetic field is calculated in wide range of temperature, electron concentration and coupling strength within the generalized self-consistent field (GSCF) approach, including the spin density correlations. The theory provides a smooth transition driven by applied magnetic field IL and temperature T from the homogeneous superconducting state into a spatially inhomogeneous state with the order parameter Delta ((-))(Q) not equal 0.

•Jan 1, 2000•0 citations
[[abstract]]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 ail n in any dimension. The developed GSCF approach in magnetic field suggests a smooth transition into the inhomogeneous superconducting state.
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.
[[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.
Ground-state properties of the attractive Hubbard model in one dimension are studied by means of both the exact Bethe-ansatz formalism and the self-consistent field (SCF) approach with renormalized chemical potential for general band fillings n and a wide range of coupling strength U/t.U/t.U/t. The energy, the concentration of double occupied sites, the kinetic energy and the chemical potential of the ground state are in a good numerical agreement with the exact results over a wide range of parameters U/tU/tU/t and n. The concentration of local pairs or double occupied sites in the Bethe-ansatz solution serves as a suitable parameter measuring the electron pairing correlations. The SCF theory provides a simple analytical relationship between the concentration of double occupied sites, the band filling and the BCS order parameter, valid for arbitrary U/tU/tU/t and n. The calculated energy gap, the BCS order parameter, the phase diagram and the compressibility are also discussed. The SCF theory in one dimension distinguishes the order parameter from the excitation gap and suggests a smooth crossover away from half-filling (at $n\ensuremath{\ne}1)$ from the BCS pairing to the Bose condensation regime under the variation of U/tU/tU/t and n.
[[abstract]]Thermodynamic characteristics of the one-dimensional attractive Hubbard model are calculated by means of the generalized self-consistent field (GSCF) approach for a wide range of interaction strength U less than or equal to, 0, in the presence of external magnetic field h greater than or equal to 0, temperature T greater than or equal to 0 and electron concentration 0 less than or equal to n less than or equal to 1. The GSCF theory shows a sharp transition driven by h > 0 and T from the uniform superconducting state into a spatially inhomogeneous state in which the order parameter Delta ((-))(q) has wave vector (0 < \q \ less than or equal to pi). The concentration of double occupied sites and the bound electron pairs with opposite spins n(pair) are calculated and we found a simple relationship between the order parameters Delta ((-))(q) and average spin s, valid for the arbitrary U, all n and h. (C) 2001 Published by Elsevier Science B.V.
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]]The thermodynamic phase diagram of the attractive Hubbard model in the presence of magnetic field is calculated in wide range of temperature, electron concentration and coupling strength within the generalized self-consistent field (GSCF) approach, including the spin density correlations. The theory provides a smooth transition driven by applied magnetic field IL and temperature T from the homogeneous superconducting state into a spatially inhomogeneous state with the order parameter Delta ((-))(Q) not equal 0.