Gap in the spin excitations and magnetization curve of the one-dimensional attractive Hubbard model

Bahder, Thomas B.; Woynarovich, F.

doi:10.1103/physrevb.33.2114

Cited by 69 publications

(66 citation statements)

References 20 publications

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“…(7) in comparison to those calculated within the exact Bethe-Ansatz equations to obtain more credibility for our parametrization formula. For this purpose, we take the derivative of the ground state energy with respect to the magnetization to calculate the magnetic field in equilibrium condition which is h(n, s, γ) = ∂[nε GS (n, ζ, γ)]/∂s [25]. The magnetization vanishes when the field becomes smaller than the critical value h c , a term associated with the spin energy gap in the attractive case (Note that it vanishes in the repulsive case.).…”

Section: The Model and Its Parametrization Resultsmentioning

confidence: 99%

Spin-density-functional theory for imbalanced interacting Fermi gases in highly elongated harmonic traps

Xianlong

Asgari

2008

Phys. Rev. A

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We numerically study imbalanced two component Fermi gases with attractive interactions in highly elongated harmonic traps. An accurate parametrization formula for the ground state energy is presented for a spin-polarized attractive Gaudin-Yang model. Our studies are based on an accurate microscopic spin-density-functional theory through the Kohn-Sham scheme which employs the onedimensional homogeneous Gaudin-Yang model with Luther-Emery-liquid ground-state correlation as a reference system. A Thomas-Fermi approximation is examined incorporating the exchangecorrelation interaction. By studying the charge and spin density profiles of the system based on these methods, we gain a quantitative understanding of the role of attractive interactions and polarization on the formation of the two-shell structure, with the coexisted Fulde-Ferrell-Larkin-Ovchinnikovtype phase in the center of the trap and either the BCS superfluid phase or the normal phase at the edges of the trap. Our results are in good agreement with the recent theoretical consequences.

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Section: The Model and Its Parametrization Resultsmentioning

confidence: 99%

Spin-density-functional theory for imbalanced interacting Fermi gases in highly elongated harmonic traps

Xianlong

Asgari

2008

Phys. Rev. A

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“…A wide variety of models fall into the Luther-Emery universality class and my results should be applicable there in a low-energy sector: Luttinger liquids coupled to phonons and related models so long as they are incommensurate, have wide regions of parameter space with gapped spin fluctuations and gapless charges 31 ; the negative-U Hubbard model at any band-filling has a spin gap 32 , and the positive-U Hubbard model at half-filling has a charge gap 33,34 ; with longer-range interactions, charge gaps can occur at different rational bandfillings, too. The t − J-model has a spin gap at low density 35 .…”

Section: )mentioning

confidence: 99%

Dynamical correlation functions of one-dimensional superconductors and Peierls and Mott insulators

Voit

1998

Eur. Phys. J. B

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I construct the spectral function of the Luther-Emery model which describes one-dimensional fermions with one gapless and one gapped degree of freedom, i.e. superconductors and Peierls and Mott insulators, by using symmetries, relations to other models, and known limits. Depending on the relative magnitudes of the charge and spin velocities, and on whether a charge or a spin gap is present, I find spectral functions differing in the number of singularities and presence or absence of anomalous dimensions of fermion operators. I find, for a Peierls system, one singularity with anomalous dimension and one finite maximum; for a superconductor two singularities with anomalous dimensions; and for a Mott insulator one or two singularities without anomalous dimension. In addition, there are strong shadow bands. I generalize the construction to arbitrary dynamical multi-particle correlation functions. The main aspects of this work are in agreement with numerical and Bethe Ansatz calculations by others. I also discuss the application to photoemission experiments on 1D Mott insulators and on the normal state of 1D Peierls systems, and propose the Luther-Emery model as the generic description of 1D charge density wave systems with important electronic correlations.

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“…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%

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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Gap in the spin excitations and magnetization curve of the one-dimensional attractive Hubbard model

Cited by 69 publications

References 20 publications

Spin-density-functional theory for imbalanced interacting Fermi gases in highly elongated harmonic traps

Spin-density-functional theory for imbalanced interacting Fermi gases in highly elongated harmonic traps

Dynamical correlation functions of one-dimensional superconductors and Peierls and Mott insulators

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

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