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

Xianlong, Gao; Asgari, Reza

doi:10.1103/physreva.77.033604

Cited by 32 publications

(29 citation statements)

References 51 publications

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“…It is clear that the TF approximation is not able to reproduce the short length-scale charge and spin fluctuations, since the local density approximation assumes a slow varying density profiles, as already pointed out in previous studies. 36,56 However, the TF boundaries of the phase separated states are in a quite good agreement with our exact QMC calculations. In order to better understand this agreement, we study the dependence of the local polarization on the number of particles N and coupling g, and compare our QMC results with the TF predictions.…”

Section: A Ground Statesupporting

confidence: 82%

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Quantum Monte Carlo study of one-dimensional trapped fermions with attractive contact interactions

2008

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Using exact continuous quantum Monte Carlo techniques, we study the zero and finite temperature properties of a system of harmonically trapped one dimensional spin 1/2 fermions with short range interactions. Motivated by experimental searches for modulated Fulde-Ferrel-Larkin-Ovchinikov states, we systematically examine the impact of a spin imbalance on the density profiles. We quantify the accuracy of the Thomas-Fermi approximation, finding that for sufficiently large particle numbers (N > ∼ 100) it quantitatively reproduces most features of the exact density profile. The Thomas-Fermi approximation fails to capture small Friedel-like spin and density oscillations and overestimates the size of the fully paired region in the outer shell of the trap. Based on our results, we suggest a range of experimentally tunable parameters to maximize the visibility of the double shell structure of the system and the Fulde-Ferrel-Larkin-Ovchinikov state in the one dimensional harmonic trap. Furthermore, we analyze the fingerprints of the attractive contact interactions in the features of the momentum and pair momentum distributions.

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Section: A Ground Statesupporting

confidence: 82%

“…The Thomas-Fermi results have been widely discussed elsewhere, and we refer the reader to previous works 22,34,35,36 for complete details. Here, we mention that Eq.…”

Section: Methodsmentioning

confidence: 99%

Quantum Monte Carlo study of one-dimensional trapped fermions with attractive contact interactions

2008

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“…Since its inception, BALDA has been applied to many different problems including disorder and critical behavior in optical lattices (Campo Jr. et al, 2009;, spin-charge separation (Vieira, 2012(Vieira, , 2014 and effects of spatial inhomogeneity (Lima et al, 2007;Silva et al, 2005) in strongly correlated systems, confined fermions both with attractive and repulsive interactions (Campo and Capelle, 2005), current DFT on a lattice (Akande and Sanvito, 2012), electric fields and strong correlation (Akande and Sanvito, 2010), and various critical phenomena in 1-D systems (Abedinpour et al, 2007a;Franca et al, 2012a). Extensions to include spindependence (BALSDA) have been principally used for studying density oscillations (Vieira et al, 2008;, and fermions in confinement (Hu et al, 2010;Xianlong, 2013;Xianlong and Asgari, 2008). A thermal DFT approximation on the lattice has been constructed using BALDA .…”

Section: B 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

123

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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“…Examples are the phase separation in a dual-species BEC [5], the collapse of the degenerate Fermi gas in a Bose-Fermi mixture [14] and the celebrated BCS-BEC crossover in a Fermi-Fermi mixture [19,20]. Those intriguing features also stimulated enormous efforts on the theoretical side, revealing, for example, the phase separation and phase diagram [21][22][23][24][25][26][27][28], the stability conditions [29][30][31][32], and the collective excitations [33][34][35] in various atomic mixtures.…”

Section: Introductionmentioning

confidence: 99%

Bunching-antibunching crossover in harmonically trapped few-body Bose-Fermi mixtures

Chen¹,

Schurer²,

Schmelcher³

2018

Phys. Rev. A

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We investigate the ground state of a few-body Bose-Fermi mixture in a one-dimensional harmonic trap with varying interaction strengths and mass ratio. A bunching-antibunching crossover of the bosonic species for increasing interspecies' repulsion is observed within our fully correlated ab initio studies. Interestingly, this crossover is suppressed if the bosonic repulsion exceeds a critical value which strongly depends on the mass ratio. In order to unveil the physical origin of this crossover, we employ different levels of approximations: while a species mean-field approach can account for the antibunching, only the inclusion of the interspecies correlations can lead to the bunching. We show that these correlations effectively create an induced bosonic interaction, which in turn elucidates the occurrence of the bosonic bunching. Finally, we derive a two-site extended Bose-Hubbard model which reveals the low-energy physics of the bosons for the case of much heavier fermions. arXiv:1805.05384v3 [cond-mat.quant-gas]

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

Cited by 32 publications

References 51 publications

Quantum Monte Carlo study of one-dimensional trapped fermions with attractive contact interactions

Quantum Monte Carlo study of one-dimensional trapped fermions with attractive contact interactions

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

Bunching-antibunching crossover in harmonically trapped few-body Bose-Fermi mixtures

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