Ground-state properties of the one-dimensional attractive Hubbard model with confinement: a comparative study

We revisit the one-dimensional attractive Hubbard model by using the Bethe-ansatz based density-functional theory and density-matrix renormalization method. The ground-state properties of this model are discussed in details for different fillings and different confining conditions in weak-to-intermediate coupling regime. We investigate the ground-state energy, energy gap, and pair-binding energy and compare them with those calculated from the canonical Bardeen-Cooper-Schrieffer approximation. We find that the Bethe-ansatz based density-functional theory is computationally easy and yields an accurate description of the ground-state properties for weak-to-intermediate interaction strength, different fillings, and confinements. In order to characterize the quantum phase transition in the presence of a harmonic confinement, we calculate the thermodynamic stiffness, the density-functional fidelity, and fidelity susceptibility, respectively. It is shown that with the increase of the number of particles or attractive interaction strength, the system can be driven from the Luther-Emery-type phase to the composite phase of Luther-Emery-like in the wings and insulating-like in the center.