Many-body perturbation theory calculations on circular quantum dots

Waltersson, Erik; Lindroth, Eva

doi:10.1103/physrevb.76.045314

Cited by 11 publications

(11 citation statements)

References 33 publications

(71 reference statements)

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“…The least studied method is however many-body perturbation theory which has been shown to be very powerful for the calculation of atomic properties. Calculations up to second order in the perturbation expansion have been made by just a few authors, 34,35 and equally few coupled-cluster calculations have been presented. [36][37][38] For small to medium sized molecules as well as atoms, the coupled-cluster(CC) method is known to successfully combine feasibility with accuracy.…”

Section: Introductionmentioning

confidence: 99%

Performance of the coupled-cluster singles and doubles method applied to two-dimensional quantum dots

2013

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An implementation of the coupled-cluster single and double excitations (CCSD) method on two-dimensional quantum dots is presented. Advantages and limitations are studied through comparison with other high accuracy approaches, including another CCSD implementation, for up to twelve confined electrons. The possibility to effectively use a very large basis set is found to be an important advantage compared to full configuration interaction implementations. The error in the ground-state energy introduced by truncating at triple excitations is shown to be comparable to the difference between the results from the variation and diffusion Monte Carlo methods. Convergence of the iterative solution of the coupled cluster equations is found for surprisingly weak confinement strengths even when the full electron-electron interaction is treated as a perturbation. The relevance of the omitted excitations is investigated through comparison with full configuration interaction results.

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Section: Introductionmentioning

confidence: 99%

Performance of the coupled-cluster singles and doubles method applied to two-dimensional quantum dots

2013

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“…Fourier expansions for algebraic distance functions have a rich history, and this expansion makes its appearance in the theory of arbitrarily-shaped charge distributions in electrostatics ( [33], [41], [5], [35], [34], [40]), magnetostatics ( [39], [6]) quantum direct and exchange Coulomb interactions ( [11], [20], [16], [32], [4]), Newtonian gravity ( [17], [37], [26], [25], [19], [31], [36], [9], [28], [7], [38]), the Laplace coefficients for planetary disturbing function ( [14], [15]), and potential fluid flow around actuator discs ( [8], [24]), just to name a few direct physical applications. A precise Fourier e imφ analysis for these applications is extremely useful to fully describe the general non-axisymmetric nature of these problems.…”

Section: Introductionmentioning

confidence: 99%

Generalized Heine’s identity for complex Fourier series of binomials

Cohl

Dominici

2010

Proc. R. Soc. A.

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In his treatise, Heine ( Heine 1881 In Theorie und Anwendungen ) gave an identity for the Fourier series of the function , with , and z >1, in terms of associated Legendre functions of the second kind . In this paper, we generalize Heine’s identity for the function , with , and , in terms of . We also compute closed-form expressions for some .

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“…These studies have used DFT [41,42], HF [43], exact diagonalization [44] and exact solutions [45][46][47]. However, despite the importance of the correlation energy, only a few studies [48][49][50] have explored the confinement effect on E c .…”

Section: Quantum Dots At High Densitymentioning

confidence: 99%

Correlation energy of anisotropic quantum dots

2011

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We study the $D$-dimensional high-density correlation energy $\Ec$ of the singlet ground state of two electrons confined by a harmonic potential with Coulombic repulsion. We allow the harmonic potential to be anisotropic, and examine the behavior of $\Ec$ as a function of the anisotropy $\alpha^{-1}$. In particular, we are interested in the limit where the anisotropy goes to infinity ($\alpha\to0$) and the electrons are restricted to a lower-dimensional space. We show that tuning the value of $\alpha$ from 0 to 1 allows a smooth dimensional interpolation and we demonstrate that the usual model, in which a quantum dot is treated as a two-dimensional system, is inappropriate. Finally, we provide a simple function which reproduces the behavior of $\Ec$ over the entire range of $\alpha$.Comment: 5 pages, 2 figures, 1 table, submitted to Phys. Rev.

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Many-body perturbation theory calculations on circular quantum dots

Cited by 11 publications

References 33 publications

Performance of the coupled-cluster singles and doubles method applied to two-dimensional quantum dots

Performance of the coupled-cluster singles and doubles method applied to two-dimensional quantum dots

Generalized Heine’s identity for complex Fourier series of binomials

Correlation energy of anisotropic quantum dots

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