Self-consistent and exact studies of pairing correlations and crossover in the one-dimensional attractive Hubbard model

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. 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/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/t and it. 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 Sap and suggests a smooth crossover away from half-filling (at n not equal 1) from the BCS pairing to the Bose condensation regime under the variation of Ult and n. [S0163-1829(99)04911-5].