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

Kocharian, Armen; Yang, Cheng‐Ta; Chiang, Yih-Cherng

doi:10.1103/physrevb.59.7458

Cited by 31 publications

(52 citation statements)

References 39 publications

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“…Substituting these series into the Lieb-Wu equations (see section 3 in [14] and section 3 in this paper) and taking the terms of the same order of magnitude, we have…”

Section: Appendix a Strong-coupling Expansionmentioning

confidence: 99%

“…For example, in an empty band (n = 0) for U < 0 the average spin s ≡ 0, so every quantity is independent of the magnetic field. In this case we have B = 0, ρ = 1/2π , Q = π , E = E h = D = E kin = χ = 0, the critical magnetic fields for spin (magnetization) onset and saturation, h c1 and h c2 (see section 5.1), are equal to each other for arbitrary coupling and [12,14,31,32] …”

Section: Strong-coupling Limitmentioning

confidence: 99%

“…The ground-state properties of the one-dimensional Hubbard model have been analysed for the case where U < 0 [9][10][11][12][13][14] and U > 0 [15][16][17][18][19] for various n. Some elementary excitations and thermodynamic characteristics, including the specific heat coefficient, have been calculated at finite temperatures [12,[20][21][22]. In the presence of a magnetic field some of the ground-state properties were investigated within the attractive [9][10][11][12] and repulsive Hubbard models [9,12,[17][18][19].…”

Section: Introductionmentioning

confidence: 99%

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Phase transitions and exact ground-state properties of the one-dimensional Hubbard model in a magnetic field

Yang

Kocharian

Chiang

2000

J. Phys.: Condens. Matter

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Abstract. The exact phase diagrams of the one-dimensional Hubbard model, both attractive and repulsive, in the presence of an arbitrary magnetic field h for various electron concentrations n and on-site interaction strengths U < 0 or U > 0 are calculated and investigated. The exact ground-state properties, namely, the ground-state energy, the average spin (magnetization), the concentration of the doubly occupied sites, the kinetic energy, the chemical potential, the spin (magnetic) susceptibility and the charge compressibility, are calculated and examined over a wide range of interaction strengths U for various h and n. It is found that the spin susceptibility at halffilling is non-analytic and changes discontinuously as U → 0. The exact theory shows the absence of a charge energy gap in the U 0 region for all n and provides, for the chemical potential, the rigorous upper and lower bounds for half-filled and empty bands respectively. The analytical results derived for the weak-coupling limit and asymptotic expansions for strong coupling are in full agreement with the numerical calculations.

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“…Substituting these series into the Lieb-Wu equations (see section 3 in [14] and section 3 in this paper) and taking the terms of the same order of magnitude, we have…”

Section: Appendix a Strong-coupling Expansionmentioning

confidence: 99%

Section: Strong-coupling Limitmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Phase transitions and exact ground-state properties of the one-dimensional Hubbard model in a magnetic field

Yang

Kocharian

Chiang

2000

J. Phys.: Condens. Matter

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“…According to Lieb and Wu [31], the ground state (GS) properties for different fillings in the thermodynamic limit are described by the coupled integral equations (for details see Refs. [32,33]). …”

Section: The Modelmentioning

confidence: 99%

Phase separation in optical lattices in a spin-dependent external potential

Chen¹,

Xianlong²

2010

Phys. Rev. A

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We investigate the phase separation in one-dimensional Fermi gases on optical lattices. The density distributions and the magnetization are calculated by means of density-matrix renormalization method. The phase separation between spin-up and spin-down atoms is induced by the interplay of the spin-dependent harmonic confinement and the strong repulsive interaction between intercomponent fermions. We find the existence of a critical repulsive interaction strength above which the phase separation evolves. By increasing the trap imbalance, the composite phase of Mott-insulating core is changed into the one of ferromagnetic insulating core, which is incompressible and originates from the Pauli exclusion principle.

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“…The DO in the homogeneous system, D hom , can be calculated exactly from the Bethe-ansatz coupled equations [13], which is shown in Fig. 2.…”

Section: Fig 2: (Color Online)mentioning

confidence: 99%

Double occupancies in confined attractive fermions on optical lattices

Xianlong

2010

Phys. Rev. A

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

Cited by 31 publications

References 39 publications

Phase transitions and exact ground-state properties of the one-dimensional Hubbard model in a magnetic field

Phase transitions and exact ground-state properties of the one-dimensional Hubbard model in a magnetic field

Phase separation in optical lattices in a spin-dependent external potential

Double occupancies in confined attractive fermions on optical lattices

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