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Acta Physica Sinica

One-dimensional spinless fermions in a confined system

Wang Chan-juan, Ahai Chen, Gao Xian-Long

Published Jan 1, 2012• 1 citation
Publisher

Abstract

According to the exact analytical Bethe-ansatz solution of the one-dimensional spin-1/2 XXZ model, we perform a numerical study of one-dimensional spinless fermions in an optical lattice in the presence of harmonic potential by using a local density approximation. We study the density profile, and obtain the -u phase diagram (here =NfV2/t is the characteristic dimensionless density and u=V/t is the interaction strength scaled in units of the hopping parameter t). With the increases of particle density and nearest-neighbour interaction, the system undergoes five different quantum phases. Through calculating the thermodynamic stiffness S, we find that it can be used as an order parameter. Its singular points can measure the quantum phase transitions in such a confined system.

DOI
10.7498/aps.61.127501

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According to the exact analytical Bethe-ansatz solution of the one-dimensional spin-1/2 XXZ model, we perform a numerical study of one-dimensional spinless fermions in an optical lattice in the presence of harmonic potential by using a local density approximation. We study the density profile, and obtain the -u phase diagram (here =NfV2/t is the characteristic dimensionless density and u=V/t is the interaction strength scaled in units of the hopping parameter t). With the increases of particle density and nearest-neighbour interaction, the system undergoes five different quantum phases. Through calculating the thermodynamic stiffness S, we find that it can be used as an order parameter. Its singular points can measure the quantum phase transitions in such a confined system.
Using the exact Bethe ansatz solution of the Hubbard model and Luttinger liquid theory, we investigate the density profiles and collective modes of one-dimensional ultracold fermions confined in an optical lattice with a harmonic trapping potential. We determine a generic phase diagram in terms of a characteristic filling factor and a dimensionless coupling constant. The collective oscillations of the atomic mass density, a technique that is commonly used in experiments, provide a signature of the quantum phase transition from the metallic phase to the Mott-insulator phase. A detailed experimental implementation is proposed.
We perform a numerical study of a one-dimensional Fermi-Hubbard model in harmonic traps within the Thomas-Fermi approximation based on the exact Bethe-ansatz solution. The $\ensuremath{\rho}\ensuremath{-}U/t$ phase diagram is shown for the systems of attractive interactions ($\ensuremath{\rho}$ is the characteristic density and U/tU/tU/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 in detecting the composite phases induced by the trapping potential are discussed in detail.
We present an extensive numerical study of the ground-state properties of confined repulsively interacting fermions in one-dimensional optical lattices. Detailed predictions for the atom-density profiles are obtained from parallel Kohn-Sham density-functional calculations and quantum Monte Carlo simulations. The density-functional calculations employ a Bethe ansatz based local-density approximation for the correlation energy that accounts for Luttinger-liquid and Mott-insulator physics. Semianalytical and fully numerical formulations of this approximation are compared with each other and with a cruder Thomas-Fermi-type local-density approximation for the total energy. Precise quantum Monte Carlo simulations are used to assess the reliability of the various local-density approximations, and in conjunction with these provide a detailed microscopic picture of the consequences of the interplay between particle-particle interactions and confinement in one-dimensional systems of strongly correlated fermions.
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.
The spectral properties of the spinless fermion model with nearest-neighbor repulsive interactions on a one-dimensional lattice are investigated using the Bethe ansatz. Although its bulk quantities are exactly the same as those of the spin-1/2 XXZ chain, the difference in the statistics of particles causes substantial effects on spectral features, such as gapless points of dispersion relations and line shapes of spectral functions. In this Letter, we clarify the origin of the differences in spectral features between fermionic and bosonic systems in terms of Bethe ansatz solutions. We also confirm that the two-string solutions have considerable spectral weights in the high-energy regime.
We study the ground state properties of ultracold fermions trapped in a one-dimensional double-well optical lattice by using the density-matrix renormalization group method. The system is described by an extended Hubbard model with alternating hopping integrals and an external harmonic confining potential. We clarify the characteristic features of the metal–insulator phase transition originating from the double-well structure of the lattices. Several different types of insulating regions coexist when the number of atoms at each site is an integer or a half integer. We found that each insulating phase except for a band insulator exhibits rather large local density fluctuations, reflecting the strong dimerization of atoms within the unit cells of double-well lattices. The phase characteristics are elucidated in detail by investigating the profiles of the local density of atoms, the local density (spin) fluctuations, the double-occupancy probability and the spatially extended sp in correlations.