Kohn-Sham density functional theory for quantum wires in arbitrary correlation regimes

Malet, Francesc; Mirtschink, André; Cremon, Jonas; Reimann, S. M.; Gori‐Giorgi, Paola

doi:10.1103/physrevb.87.115146

Cited by 47 publications

(155 citation statements)

References 78 publications

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“…As a consequence, this force can be written in terms of the negative gradient of some one-body local potential v SCE (r), 15 such that…”

Section: The Ks Sce Approachmentioning

confidence: 99%

“…The starting point is the so-called strictly-correlated-electrons (SCE) reference system, introduced by Seidl and coworkers, [11][12][13] which has the same density as the real interacting one, but in which the electrons are infinitely correlated instead of non-interacting. The SCE functional has a highly non-local dependence on the density, but its functional derivative can be easily constructed, 14,15 yielding a local one-body potential which can be used in the Kohn-Sham scheme to approximate the exchange-correlation term. The SCE functional tends asymptotically to the exact Hartree-exchange-correlation functional in the extreme infinite correlation (or low-density) limit.…”

Section: Introductionmentioning

confidence: 99%

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Exchange–correlation functionals from the strong interaction limit of DFT: applications to model chemical systems

Malet

Mirtschink

Giesbertz

et al. 2014

Phys. Chem. Chem. Phys.

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We study model one-dimensional chemical systems (representative of their three-dimensional counterparts) using the strictly-correlated electrons (SCE) functional, which, by construction, becomes asymptotically exact in the limit of infinite coupling strength. The SCE functional has a highly non-local dependence on the density and is able to capture strong correlation within KohnSham theory without introducing any symmetry breaking. Chemical systems, however, are not close enough to the strong-interaction limit so that, while ionization energies and the stretched H2 molecule are accurately described, total energies are in general way too low. A correction based on the exact next leading order in the expansion at infinite coupling strength of the Hohenberg-Kohn functional largely improves the results.

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“…As a consequence, this force can be written in terms of the negative gradient of some one-body local potential v SCE (r), 15 such that…”

Section: The Ks Sce Approachmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Exchange–correlation functionals from the strong interaction limit of DFT: applications to model chemical systems

Malet

Mirtschink

Giesbertz

et al. 2014

Phys. Chem. Chem. Phys.

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“…This provides an effective single-particle potential in a rigorous and physical way [35][36][37] relying on calculations of the uniform system energy by means of other many-body approaches. The formalism becomes asymptotically exact in the limits of both vanishing and extremely strong coupling.…”

mentioning

confidence: 99%

“…For the Coulomb interaction, this functional has been widely studied [33,39,40], and it has been shown to be able to capture the physics of the strongly-correlated regime in model quantum wires and quantum dots [35][36][37], yielding results beyond the mean-field level. The construction of V SCP int [n] for a given density n(r) is equivalent to an optimal transport (or mass transportation theory, a wellestablished field of mathematics and economics) problem with cost given by the interaction [41,42].…”

mentioning

confidence: 99%

“…[52] for a discussion on contact interactions). The SCP functional is thus naturally very well suited for ionic gases in the strong-correlation regime, where it is expected to provide a large part of the total interaction energy [35][36][37]. Even more interesting is the case of general dipolar anisotropic interactions: the SCP functional combined with the KS kinetic energy (fermionic or bosonic) should be able to capture many of the interesting phenomena observed in the strongcorrelation regime [29,53].…”

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confidence: 99%

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Density-Functional Theory for Strongly Correlated Bosonic and Fermionic Ultracold Dipolar and Ionic Gases

et al. 2015

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We introduce a density functional formalism to study the ground-state properties of stronglycorrelated dipolar and ionic ultracold bosonic and fermionic gases, based on the self-consistent combination of the weak and the strong coupling limits. Contrary to conventional density functional approaches, our formalism does not require a previous calculation of the interacting homogeneous gas, and it is thus very suitable to treat systems with tunable long-range interactions. Due to its asymptotic exactness in the regime of strong correlation, the formalism works for systems in which standard mean-field theories fail.Introduction -In contrast with its widespread use and success in areas as diverse as quantum chemistry [1], materials science [2] or semiconductor nanostructures [3], Density Functional Theory (DFT) has received relatively little attention in the very active field of ultracold atomic gases. It is well known that the Hohenberg-Kohn theorems, originally formulated in terms of the electron gas [4,5], hold for both fermionic and bosonic systems, as well as for interactions different than the Coulomb one. However, the lack of adequate density functionals has hindered the role of DFT in the study of ultracold atomic gases in favour of other well-established approaches, such as the widely used Gross-Pitaevskii (GP) method in the case of Bose gases. The latter is a mean-field approach and does not allow treating the effect of correlations, which play a crucial role in many different phenomena occurring in ultracold quantum gases [6]. One then often turns to configuration-interaction (CI), quantum Monte Carlo (QMC) or Green's-function methods (for recent reviews, see, e.g., Refs. 6-8).

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Kondo effect in the Kohn–Sham conductance of multiple‐level quantum dots

Stefanucci

Kurth

2013

Physica Status Solidi (b)

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At zero temperature, the Landauer formalism combined with static density functional theory is able to correctly reproduce the Kondo plateau in the conductance of the Anderson impurity model provided that an exchangecorrelation potential is used which correctly exhibits steps at integer occupation. Here we extend this recent finding to multi-level quantum dots described by the constant-interaction model. We derive the exact exchange-correlation potential in this model for the isolated dot and deduce an accurate approximation for the case when the dot is weakly coupled to two leads. We show that at zero temperature and for non-degenerate levels in the dot we correctly obtain the conductance plateau for any odd number of electrons on the dot. We also analyze the case when some of the levels of the dot are degenerate and again obtain good qualitative agreement with results obtained with alternative methods. As in the case of a single level, for temperatures larger than the Kondo temperature, the Kohn-Sham conductance fails to reproduce the typical Coulomb blockade peaks. This is attributed to dynamical exchangecorrelation corrections to the conductance originating from time-dependent density functional theory.Copyright line will be provided by the publisher 1 Introduction Common wisdom has it that Density Functional Theory (DFT) is not able to describe strongly correlated systems although the fundamental theorems of DFT apply to these systems as well. In fact, the difficulties of dealing with strong correlations are not inherent to DFT but to the DFT approximations. In the last years there has been considerable progress in understanding which features a DFT approximation should have in order to capture strong correlation effects [1][2][3][4][5][6][7][8][9][10][11][12][13], and the derivative discontinuity of the exchange-correlation energy functional [14] has emerged as one of the key properties. In the context of quantum transport the derivative discontinuity turned out to be crucial to reproduce the conductance plateau [15][16][17] due to the Kondo effect, a hallmark of strong correlations.

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Kohn-Sham density functional theory for quantum wires in arbitrary correlation regimes

Cited by 47 publications

References 78 publications

Exchange–correlation functionals from the strong interaction limit of DFT: applications to model chemical systems

Exchange–correlation functionals from the strong interaction limit of DFT: applications to model chemical systems

Density-Functional Theory for Strongly Correlated Bosonic and Fermionic Ultracold Dipolar and Ionic Gases

Kondo effect in the Kohn–Sham conductance of multiple‐level quantum dots

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