Müller’s exchange-correlation energy in density-matrix-functional theory

Frank, Rupert L.; Lieb, Élliott H.; Seiringer, Robert; Siedentop, Heinz

doi:10.1103/physreva.76.052517

Cited by 60 publications

(100 citation statements)

References 39 publications

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“…Müller's functional satisfies both conditions 20 for all p with 0 Ͻ p Ͻ 1. All studies of this functional to date have set p =1/ 2 ͑in the rest of the paper we refer to this as the Müller functional͒.…”

Section: ͑1͒mentioning

confidence: 99%

Reduced density matrix functional for many-electron systems

et al. 2008

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Reduced density matrix functional theory for the case of solids is presented and an exchange-correlation functional based on a fractional power of the density matrix is introduced. We show that compared to other functionals, this produces more accurate behavior for total energies as a function of particle number for finite systems. Moreover, it captures the correct band-gap behavior for conventional semiconductors, as well as strongly correlated Mott insulators, where a gap is obtained in the absence of any magnetic ordering. DOI: 10.1103/PhysRevB.78.201103 PACS number͑s͒: 71.10.Ϫw, 71.20.Nr, 71.27.ϩa, 71.45.Gm One of the most dramatic failures of the usual localdensity approximation ͑LDA͒ or generalized-gradient-type approximations to the exchange-correlation ͑xc͒ functional of density-functional theory ͑DFT͒ is the incorrect prediction of a metallic ground state for the strongly correlated Mott insulators, of which transition-metal oxides ͑TMOs͒ may be considered as prototypical. For some TMOs ͑NiO and MnO͒ spin-polarized calculations do show a very small band gap ͑up to 95% smaller than experiments͒ but only as the result of antiferromagnetic (AFM) ordering; however, all TMOs are found to be metallic in a spin-unpolarized treatment. On the other hand, it is well known experimentally that these materials are insulating in nature even at elevated temperatures ͑much above the Néel temperature͒. 1 This indicates that the magnetic order is not the driving mechanism for the gap and is just a co-occurring phenomenon. A real challenge for any kind of ab initio theory then is the prediction of an insulating state for these strongly correlated materials in the absence of magnetic order. Until now the main focus of reduced density matrix functional theory ͑RDMFT͒ has been on finite systems such as atoms and molecules 2-11 with various xc functionals, [3][4][5][6][7][8][11][12][13][14][15] which are essentially modifications of the original Müller functional. 2 In the present work we extend RDMFT to the case of solid-state systems and introduce a functional which generates not only accurate gaps for conventional semiconductors, but demonstrates insulating behavior for Mott-type insulators in the nonmagnetic phase.Formally, the one-body reduced density matrix ␥ for a pure state of N electrons is defined as ͑spin degrees of freedom are omitted for simplicity͒ ␥͑r,rЈ͒ = N ͵ ⌿͑r,r 2 , ... ,r N ͒⌿ ‫ء‬ ͑rЈ,r 2 , ... ,r N ͒d 3 r 2 , ... ,d 3 r N . ͑1͒Diagonalization of this matrix produces a set of natural orbitals, 16 i , and occupation numbers, n i , leading to the spectral representationwhere the necessary and sufficient conditions for ensemble N representability 17 require 0 Յ n i Յ 1 for all i, and ͚ i n i = N. In terms of ␥, the total ground-state energy of the interacting system is 18 ͑atomic units are used throughout͒where ͑r͒ = ␥͑r , r͒, V is a given external potential, and E xc is what we call the xc energy functional. Minimizing the total energy with E xc ͓␥͔ =− 1 2 ͉͐␥͑r , rЈ͉͒ 2 / ͉r − rЈ͉d 3 rd 3 rЈ is equival...

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Section: ͑1͒mentioning

confidence: 99%

Reduced density matrix functional for many-electron systems

et al. 2008

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“…4,15,28 It was recently shown by Frank et al 36 that for two electron systems the Müller functional provides a lower-bound for the total energy. They also showed that, for this functional, the total energy does not go to zero if the ionic potential is switched off but to the value −N/8 a.u.…”

Section: Functionalsmentioning

confidence: 99%

Benchmark calculations for reduced density-matrix functional theory

Lathiotakis

Marques

2008

The Journal of Chemical Physics

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Reduced density-matrix functional theory (RDMFT) is a promising alternative approach to the problem of electron correlation. Like standard density functional theory, it contains an unknown exchange-correlation functional, for which several approximations have been proposed in the last years. In this article, we benchmark some of these functionals in an extended set of molecules with respect to total and atomization energies. Our results show that the most recent RDMFT functionals give very satisfactory results compared to more involved quantum chemistry and density functional approaches.

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“…In particular, we perform self-consistent Hartree-Fock (HF) calculations and, in addition, study a similar self-consistent variational procedure using the so-called Müller density matrix functional (replacing the Fock term). 30,31 In atomic physics applications, the Müller functional is sometimes superior to the HF approach and is valuable because it yields a lower bound for the ground-state energy. 31 We note that HF calculations for graphene dots with infinite-mass confine-ment have also been carried out by other groups.…”

Section: Introductionmentioning

confidence: 99%

Signatures of Wigner molecule formation in interacting Dirac fermion quantum dots

2011

Self Cite

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We study N interacting massless Dirac fermions confined in a two-dimensional quantum dot. Physical realizations of this problem include a graphene monolayer and the surface state of a strong topological insulator. We consider both a magnetic confinement and an infinite mass confinement. The ground state energy is computed as a function of the effective interaction parameter α from the Hartree-Fock approximation and, alternatively, by employing the Müller exchange functional. For N = 2, we compare those approximations to exact diagonalization results. The Hartree-Fock energies are highly accurate for the most relevant interaction range α 2, but the Müller functional leads to an unphysical instability when α 0.756. Up to 20 particles were studied using HartreeFock calculations. Wigner molecule formation was observed for strong but realistic interactions, accompanied by a rich peak structure in the addition energy spectrum.

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Müller’s exchange-correlation energy in density-matrix-functional theory

Cited by 60 publications

References 39 publications

Reduced density matrix functional for many-electron systems

Reduced density matrix functional for many-electron systems

Benchmark calculations for reduced density-matrix functional theory

Signatures of Wigner molecule formation in interacting Dirac fermion quantum dots

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