On the computation of electronic correlation energies within the local approach

Stollhoff, Gernot; Fulde, Peter

doi:10.1063/1.440693

Cited by 248 publications

(89 citation statements)

References 17 publications

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“…A similar ferromagnetic superexchange interaction can be assumed between β-cage clusters via the 109.5 • orthogonalized sp 3 orbitals with the T d symmetry of supercage clusters in the ferromagnetism of K n /Na 7.3 K 4.7 -LSX. A similar electron correlation in the sp 3 hybridized state has been calculated in CH 4 molecule [108,109].…”

Section: Ferrimagnetism and Ferromagnetism In Na-k Alloy System In Zesupporting

confidence: 48%

Electrons of alkali metals in regular nanospaces of zeolites

Nakano

Nozue

2017

Advances in Physics: X

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The s-electrons of alkali metals loaded into regular nanospaces (nanocages) of zeolite crystals display novel electronic properties, such as a ferrimagnetism, a ferromagnetism, an antiferromagnetism, an insulator-to-metal transition, etc., depending on the kind of alkali metals, their loading density, and the structure type of zeolite frameworks. These properties are entirely different from those in bulk alkali metals of freeelectrons. Alkali-metal clusters are stabilized in cages of zeolites, and new quantum states of s-electrons, such as 1s, 1p, and 1d states in the spherical quantum-well model, are formed. An electron correlation, a polaron effect, and an orbital degeneracy in the quantum states of s-electrons play critical roles in taking on the novel electronic properties. Electronic properties can be overviewed systematically by a coarse-grained model of localized s-electron states in cages based on the tightbinding approximation, followed by the t-U-S-n diagram of the correlated polaron system given by the so-called HolsteinHubbard Hamiltonian: an electron transfer energy through windows of cages (t), a Coulomb repulsion energy between two s-electrons in the same cage (U), a short-range electron-phonon interaction energy due to the cation displacements (S), and an average number of s-electrons per cage (n). Beyond the jellium background model of alkali-metal clusters, a huge spin-orbit interaction has been observed in the 1p degenerate orbitals of clusters, similarly to the Rashba mechanism. ARTICLE HISTORY

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Section: Ferrimagnetism and Ferromagnetism In Na-k Alloy System In Zesupporting

confidence: 48%

Electrons of alkali metals in regular nanospaces of zeolites

Nakano

Nozue

2017

Advances in Physics: X

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“…In the Quantum Monte Carlo (QMC) approach 3 , one multiplies a mean field function (Slater determinante) by a Jastrow factor which explicitly introduces inter-electronic coordinates. Another approach of incorporating electron correlation is the local ansatz (LA) 4 , where local operators acting on the SCF wave-function are used to admix suitable one-and two-particle excitations to the meanfield ground state. A method closely related to the ideas of the LA is the incremental expansion of the correlation energy; here information on local excitations in clusters is made use of, which are accessible to an accurate quantum-chemical configuration interaction (CI) treatment.…”

Section: Introductionmentioning

confidence: 99%

Electron correlations for ground-state properties of group-IV semiconductors

1995

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“…JastrowGutzwiller correlation factors are also very popular as variational wave functions in quantum Monte Carlo and other applications [7][8][9][10][11][12][13][14][15]. Non-variational solutions have also been discussed in the literature.…”

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confidence: 99%

Lie algebraic similarity transformed Hamiltonians for lattice model systems

et al. 2015

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We present a class of Lie algebraic similarity transformations generated by exponentials of twobody on-site hermitian operators whose Hausdorff series can be summed exactly without truncation. The correlators are defined over the entire lattice and include the Gutzwiller factor n i↑ n i↓ , and twosite products of density (n i↑ + n i↓ ) and spin (n i↑ − n i↓ ) operators. The resulting non-hermitian many-body Hamiltonian can be solved in a biorthogonal mean-field approach with polynomial computational cost. The proposed similarity transformation generates locally weighted orbital transformations of the reference determinant. Although the energy of the model is unbound, projective equations in the spirit of coupled cluster theory lead to well-defined solutions. The theory is tested on the 1D and 2D repulsive Hubbard model where it yields accurate results for small and medium size interaction strengths.Introduction.-Hamiltonian similarity transformations are ubiquitous in many areas of physics, including electronic structure and condensed matter theories, and have been applied in a myriad of contexts [1][2][3][4][5][6]. JastrowGutzwiller correlation factors are also very popular as variational wave functions in quantum Monte Carlo and other applications [7][8][9][10][11][12][13][14][15]. Non-variational solutions have also been discussed in the literature. Tsuneyuki [16] presented a Hilbert space Jastrow method based on a Gutzwiller factor i n i↑ n i↓ and applied it to the 1D Hubbard model, minimizing its energy variance as in the transcorrelated method [17][18][19]. Neuscamman et al. [20] proposed many-body Jastrow correlators, diagonal in the lattice basis, and truncated them to a subset of sites matching a given pattern; these authors compared projective solutions with those obtained stochastically via Monte Carlo.Here, we consider Hamiltonian transformations of the form e −J He J based on hermitian correlators J built from general two-body products of on-site operators over the entire lattice. The transformations here are generated by density (charge), spin, and Gutzwiller factor correlators, including density-spin crossed terms. Similar Jastrowtype correlators have been extensively discussed in the literature but almost always in a variational context [10]. Our transformed Hamiltonian is non-hermitian but can be solved in mean-field via projective equations similar in spirit to those of coupled cluster theory [20,21]. In this sense, the model is an extension that fits under the generalized coupled cluster label [22][23][24]. The fundamental difference is that traditional coupled cluster is formulated with particle-hole excitations out of a reference determinant via a non-hermitian cluster operator; the present model is constructed with on-site hermitian correlators.The main result of this paper is the realization that the Hausdorff series resulting from the non-unitary similarity transformation e −J He J can be analytically summed. This result follows from Lie algebraic arguments [25] after recognizing that bot...

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On the computation of electronic correlation energies within the local approach

Cited by 248 publications

References 17 publications

Electrons of alkali metals in regular nanospaces of zeolites

Electrons of alkali metals in regular nanospaces of zeolites

Electron correlations for ground-state properties of group-IV semiconductors

Lie algebraic similarity transformed Hamiltonians for lattice model systems

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