Natural occupation numbers in two-electron quantum rings

Within density-functional theory, the local-density approximation (LDA) correlation functional is typically built by fitting the difference between the near-exact and Hartree-Fock (HF) energies of the uniform electron gas (UEG), together with analytic perturbative results from the high-and low-density regimes. Near-exact energies are obtained by performing accurate diffusion Monte Carlo calculations, while HF energies are usually assumed to be the Fermi fluid HF energy. However, it has been known since the seminal work of Overhauser that one can obtain lower, symmetry-broken (SB) HF energies at any density. Here, we have computed the SBHF energies of the one-dimensional UEG and constructed a SB version of the LDA (SBLDA) from the results. We compare the performance of the LDA and SBLDA functionals when applied to one-dimensional systems, including atoms and molecules. Generalization to higher dimensions is also discussed.

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“…A 1D UEG is constructed by confining a number n of interacting electrons to a ring of radius R of electronic density 7,9,92,93…”

Section: One-dimensional Uniform Electron Gasmentioning

confidence: 99%

Symmetry-broken local-density approximation for one-dimensional systems

2016

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“…The goal of this work is therefore two-fold: i) We remove any border effects by confining the electrons to a ring [17][18][19][20] by placing the three-dimensional gaussians along the ring perimeter, and ii) We wrote a computer code that is specifically dedicated to treat low densities which allows us to reach ring perimeters as large as 10 6 Bohr (≈ 0.05 mm). We note that by confining the electrons to a ring also removes the need to add a positive background.…”

Section: Introductionmentioning

confidence: 99%

A Wigner molecule at extremely low densities: a numerically exact study

et al. 2019

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In this work we investigate Wigner localization at very low densities by means of the exact diagonalization of the Hamiltonian. This yields numerically exact results. In particular, we study a quasi-one-dimensional system of two electrons that are confined to a ring by three-dimensional gaussians placed along the ring perimeter. To characterize the Wigner localization we study several appropriate observables, namely the two-body reduced density matrix, the localization tensor and the particle-hole entropy. We show that the localization tensor is the most promising quantity to study Wigner localization since it accurately captures the transition from the delocalized to the localized state and it can be applied to systems of all sizes.

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“…The condition of quasi-exactly solvable means that the spectrum and the eigenfunction are exactly known in a discrete set of the Hamiltonian parameters. Recently there has been a flurry of activity in this subject [10,18,[27][28][29], while early examples, dealing with the same quasi-exactly solvable model, can be found in the works of Kais et. al.…”

Section: Introductionmentioning

confidence: 99%

“…The broad application to many different problems in classical and quantum physics of the Heun'equations and its polynomial solutions has been made possible by the work of Fiziev [33], in particular to the dynamics of a rotor vibratory giroscope [34], the calculation of natural occupation numbers in two electron quantum-rings [27], the solution of the Schrödinger equation for a particle trapped in a hyperbolic double-well potential [28], the problem of two electrons confined on a hypersphere [18], one electron in crossed inhomogeneous magnetic and homogeneous electric fields [29], and in the study of normal modes in non-rotating black holes [35]. The recent and salient role played by the Heun functions, and its foreseeable future, in natural sciences is depicted in the Introduction of Ref.…”

Section: Introductionmentioning

confidence: 99%

Quasi-exact solvability and entropies of the one-dimensional regularised Calogero model

Pont¹,

Osenda²,

Serra³

2018

J. Phys. A: Math. Theor.

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The divergence in the interaction term of the Calogero model can be prevented introducing a cutoff length parameter, this modification leads to a quasi-exactly solvable model whose eigenfunctions can be written in terms of Heun's polynomials. It is shown both, analytical and numerically.that the reduced density matrix obtained tracing out one particle from the two-particle density operator can be obtained exactly as well as its entanglement spectrum. The number of non-zero eigenvalues in these cases is finite. Besides, it is shown that taking the limit in which the cutoff distance goes to zero, the reduced density matrix and finite entanglement spectrum of the Calogero model is retrieved. The entanglement Rényi entropy is also studied to characterize the physical traits of the model. It is found that the quasi-exactly solvable character of the model is put into evidence by the entanglement entropies when they are calculated numerically over the parameter space of the model.

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Natural occupation numbers in two-electron quantum rings

Cited by 10 publications

References 57 publications

Symmetry-broken local-density approximation for one-dimensional systems

Symmetry-broken local-density approximation for one-dimensional systems

A Wigner molecule at extremely low densities: a numerically exact study

Quasi-exact solvability and entropies of the one-dimensional regularised Calogero model

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