Density-functional theory for the spin-1 bosons in a one-dimensional harmonic trap

Wang, Hongmei; Zhang, Yunbo

doi:10.1103/physreva.88.023626

Cited by 8 publications

(4 citation statements)

References 78 publications

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“…There has been significant interest in using BALDA to understand the derivative discontinuity in both DFT and TD-DFT [123,245,248,252]. Additionally, the BALDA approach has been developed for other BA-solvable fermionic lattice systems aside from the Hubbard model [3,156,198,246], such as the Anderson model [24,122,139], as well as bosonic systems [85,238,239].…”

Section: Baldamentioning

confidence: 99%

The Hubbard dimer: a density functional case study of a many-body problem

Carrascal

Ferrer

Smith

et al. 2015

J. Phys.: Condens. Matter

120

185

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This review explains the relationship between density functional theory and strongly correlated models using the simplest possible example, the two-site Hubbard model. The relationship to traditional quantum chemistry is included. Even in this elementary example, where the exact ground-state energy and site occupations can be found analytically, there is much to be explained in terms of the underlying logic and aims of Density Functional Theory. Although the usual solution is analytic, the density functional is given only implicitly. We overcome this difficulty using the Levy-Lieb construction to create a parametrization of the exact function with negligible errors. The symmetric case is most commonly studied, but we find a rich variation in behavior by including asymmetry, as strong correlation physics vies with charge-transfer effects. We explore the behavior of the gap and the many-body Green's function, demonstrating the 'failure' of the Kohn-Sham method to reproduce the fundamental gap. We perform benchmark calculations of the occupation and components of the KS potentials, the correlation kinetic energies, and the adiabatic connection. We test several approximate functionals (restricted and unrestricted Hartree-Fock and Bethe Ansatz Local Density Approximation) to show their successes and limitations. We also discuss and illustrate the concept of the derivative discontinuity. Useful appendices include analytic expressions for Density Functional energy components, several limits of the exact functional (weak-and strong-coupling, symmetric and asymmetric), the Kohn-Sham hopping energy functional for 3 sites, various adiabatic connection results, proofs of exact conditions for this model, and the origin of the Hubbard model from a minimal basis model for stretched H 2 .

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Section: Baldamentioning

confidence: 99%

The Hubbard dimer: a density functional case study of a many-body problem

Carrascal

Ferrer

Smith

et al. 2015

J. Phys.: Condens. Matter

120

185

View full text Add to dashboard Cite

show abstract

“…These states, either degenerate for U 2 = 0 and U 0 → ∞ or quasi-degenerate for the other cases, correspond to different density profiles of the three components with spin m = +1, 0, −1 (see [164]). A detailed density functional study with up to N = 30 atoms concluded that the competition between the repulsive density-density interactions, U 0 , and the spin-exchange interactions, U 2 , led to compli-cated density distributions of the three spin components, even when both are kept equal [198]. Note that, in that case, U 2 had the same sign as U 0 , corresponding to the antiferromagnetic case.…”

Section: Spinor Bose Mixturesmentioning

confidence: 99%

One-dimensional mixtures of several ultracold atoms: a review

Sowiński¹,

2019

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Recent theoretical and experimental progress on studying one-dimensional systems of bosonic, fermionic, and Bose-Fermi mixtures of a few ultracold atoms confined in traps is reviewed in the broad context of mesoscopic quantum physics. We pay special attention to limiting cases of very strong or very weak interactions and transitions between them. For bosonic mixtures, we describe the developments in systems of three and four atoms as well as different extensions to larger numbers of particles. We also briefly review progress in the case of spinor Bose gases of a few atoms. For fermionic mixtures, we discuss a special role of spin and present a detailed discussion of the two-and three-atom cases. We discuss the advantages and disadvantages of different computation methods applied to systems with intermediate interactions. In the case of very strong repulsion, close to the infinite limit, we discuss approaches based on effective spin chain descriptions. We also report on recent studies on higherspin mixtures and inter-component attractive forces. For both statistics, we pay particular attention to impurity problems and mass imbalance cases. Finally, we describe the recent advances on trapped Bose-Fermi mixtures, which allow for a theoretical combination of previous concepts, well illustrating the importance of quantum statistics and inter-particle interactions. Lastly, we report on fundamental questions related to the subject which we believe will inspire further theoretical developments and experimental verification. :1903.12189v3 [cond-mat.quant-gas] CONTENTS arXiv

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“…Immediately after the realization of optical lattice [5], confining spinor bosons in optical lattices becomes one of the hottest research topics in the field of cold atoms and has been extensively investigated [6][7][8][9][10], although the experimental realization of the optical lattice spinor Bose system has been achieved only very recently [11].…”

Section: Introductionmentioning

confidence: 99%

“…Since it was proposed theoretically [1,2] and realized exper imentally [3], spinor Bose-Einstein condensate has opened a new avenue to investigate magnetic systems by utilizing ultra cold atomic gases [4]. Immediately after the realization of optical lattice [5], confining spinor bosons in optical lattices becomes one of the hottest research topics in the field of cold atoms and has been extensively investigated [6][7][8][9][10], although the experimental realization of the optical lattice spinor Bose system has been achieved only very recently [11].…”

Section: Introductionmentioning

confidence: 99%

Quantum phase diagrams and time-of-flight pictures of spin-1 Bose systems in honeycomb optical lattices

Zhang

Jiang

2016

Laser Phys.

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By treating the hopping parameter as a perturbation, with the help of cumulant expansion and the resumming technique, the oneparticle Green's function of a spin1 Bose system in a honeycomb optical lattice is calculated analytically. By the use of the resummed Green's function, the quantum phase diagrams of the system in ferromagnetic cases as well as in antiferromagnetic cases are determined. It is found that in antiferromagnetic cases the Mott insulating states with even filling factor are more robust against the hopping parameter than that with odd filling factor, in agreement with results via other different approaches. Moreover, in order to illustrate the effectiveness of the resummed Green's function method in calculating timeofflight pictures, the momentum distribution function of a honeycomb lattice spin1 Bose system in the antiferromagnetic case is also calculated analytically and the corresponding timeofflight absorption pictures are plotted.

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Density-functional theory for the spin-1 bosons in a one-dimensional harmonic trap

Cited by 8 publications

References 78 publications

The Hubbard dimer: a density functional case study of a many-body problem

The Hubbard dimer: a density functional case study of a many-body problem

One-dimensional mixtures of several ultracold atoms: a review

Quantum phase diagrams and time-of-flight pictures of spin-1 Bose systems in honeycomb optical lattices

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