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

Ground-state properties of the attractive Hubbard model in one dimension ar e studied by means of both the exact Bethe-ansatz formalism and the self-co nsistent field (SCF) approach with renormalized chemical potential for gene ral 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 chem ical potential of the ground state are in a good numerical agreement with t he exact results over a wide range of parameters U/t and n. The concentrati on of local pairs or double occupied sites in the Bethe-ansatz solution ser ves as a suitable parameter measuring the electron pairing correlations. Th e SCF theory provides a simple analytical relationship between the concentr ation of double occupied sites, the band filling and the BCS order paramete r, valid for arbitrary U/t and it. The calculated energy gap, the BCS order parameter, the phase diagram and the compressibility are also discussed. T he SCF theory in one dimension distinguishes the order parameter from the e xcitation 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].