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 in 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-type in the wings and insulatinglike in the center.
We perform a numerical study of a one-dimensional Fermion-Hubbard model in harmonic traps within the Thomas-Fermi approximation based on the exact Bethe-ansatz solution. The ρ − U/t phase diagram is shown for the systems of attractive interactions (ρ is the characteristic density and U/t the interaction strength scaled in units of the hopping parameter.). We study the double occupancy, the local central density and their derivatives. Their roles are discussed in details in detecting the composite phases induced by the trapping potential.PACS numbers: 05.30. Fk,03.75.Ss,71.10.Pm,71.15.Pd The recent remarkable experimental progress in cooling and manipulating ultracold atomic gases in optical lattices provides us an alternative way to investigate the many-body effects in condensed matter system [1]. For the optical lattices loaded with atomic gases, the on-site interaction between different species can be tuned to be very strong by means of a technique named Feshbach resonance [2] or by increasing the lattice depth to decrease the hopping between neighbor sites. Thus the outstanding controllability offers the possibility to use these systems to "quantum simulate" quantum manybody physics in a well-controlled way. An example is the experimentally realized Tonks-Girardeau gas in a onedimensional (1D) optical lattice [3].In the experiments, the trapping potential used to confine atoms induces inhomogeneity and complexity in characterizing the quantum phases. Though a few techniques exist in experiments observing the new quantum phases and probing various properties in ultracold gases in optical lattices, such as the time-of-flight imaging of the momentum distribution, noise correlations and Bragg spectroscopy [1], there are difficulties in observing the composite phases induced by the inherent trapping potential, for example, the incompressible bulk Mott-and band-insulating phases surrounded by the compressible fluid phases at the edges in the 1D Fermi-Hubbard model under harmonic confinement. Scarola et al. proposed to use the core compressibility by filtering out the edge effects, which offers a direct probe of incompressible phases independent of inhomogeneity [4]. Duan et al. suggested to use the Fourier sampling of time-of-flight images to reveal new correlation functions [5]. Kollath et al. used the double occupancy (DO) induced by periodic lattice modulations via the creation of molecules to identify the pairbinding energy and the spin-ordering in a Fermi gas in an optical lattice [6], which was recently measured in the experiments by molecule formation and used to identify an incompressible Mott-insulator phase of two hyperfine states of strongly repulsive fermionic 40 K atoms [7]. The * Electronic address: gaoxl@zjnu.edu.cn compressibility of the quantum gas in the trap was used recently in identifying the incompressible Mott-insulating phase at strong interactions by independent control of external confinement and lattice depth [8]. Here in this paper we discuss how to characterize the different composit...
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