Accuracy of the Hartree-Fock method for Wigner molecules at high magnetic fields

Szafran, B.; Bednarek, S.; Adamowski, J.; Tavernier, M.; Anisimovas, Egidijus; Peeters, F. M.

doi:10.1140/epjd/e2003-00320-5

Cited by 14 publications

(3 citation statements)

References 42 publications

(170 reference statements)

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“…Vast literature is available concerning mean-field studies of electrons in quantum dots. Such publications are divided mainly into applications of density functional theory [3,[91][92][93][94][95][96] and the use of Hartree-Fock methods [20,25,27,93,[97][98][99][100][101][102][103][104]. The latter include treatments according to the restricted Hartree-Fock [97], unrestricted Hartree-Fock with spin, but not space, symmetry breaking [98][99][100], unrestricted Hartree-Fock with spin and/or space symmetry breaking [20,25,27,93,[101][102][103] and the so-called Brueckner Hartree-Fock [104,105].…”

Section: Mean-field Description and Unrestricted Hartree-fockmentioning

confidence: 99%

Symmetry breaking and quantum correlations in finite systems: studies of quantum dots and ultracold Bose gases and related nuclear and chemical methods

Yannouleas¹,

Landman²

2007

Rep. Prog. Phys.

236

358

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Investigations of emergent symmetry breaking phenomena occurring in small finite-size systems are reviewed, with a focus on the strongly correlated regime of electrons in two-dimensional semiconductor quantum dots and trapped ultracold bosonic atoms in harmonic traps. Throughout the review we emphasize universal aspects and similarities of symmetry breaking found in these systems, as well as in more traditional fields like nuclear physics and quantum chemistry, which are characterized by very different interparticle forces. A unified description of strongly correlated phenomena in finite systems of repelling particles (whether fermions or bosons) is presented through the development of a two-step method of symmetry breaking at the unrestricted Hartree–Fock level and of subsequent symmetry restoration via post Hartree–Fock projection techniques. Quantitative and qualitative aspects of the two-step method are treated and validated by exact diagonalization calculations. Strongly-correlated phenomena emerging from symmetry breaking include the following. Chemical bonding, dissociation and entanglement (at zero and finite magnetic fields) in quantum dot molecules and in pinned electron molecular dimers formed within a single anisotropic quantum dot, with potential technological applications to solid-state quantum-computing devices. Electron crystallization, with particle localization on the vertices of concentric polygonal rings, and formation of rotating electron molecules (REMs) in circular quantum dots. Such electron molecules exhibit ro-vibrational excitation spectra, in analogy with natural molecules. At high magnetic fields, the REMs are described by parameter-free analytic wave functions, which are an alternative to the Laughlin and composite-fermion approaches, offering a new point of view of the fractional quantum Hall regime in quantum dots (with possible implications for the thermodynamic limit). Crystalline phases of strongly repelling bosons. In rotating traps and in analogy with the REMs, such repelling bosons form rotating boson molecules (RBMs). For a small number of bosons, the RBMs are energetically favored compared with the Gross–Pitaevskii solutions describing vortex formation. We discuss the present status concerning experimental signatures of such strongly correlated states, in view of the promising outlook created by the latest experimental improvements that are achieving unprecedented control over the range and strength of interparticle interactions.

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Section: Mean-field Description and Unrestricted Hartree-fockmentioning

confidence: 99%

Symmetry breaking and quantum correlations in finite systems: studies of quantum dots and ultracold Bose gases and related nuclear and chemical methods

Yannouleas¹,

Landman²

2007

Rep. Prog. Phys.

236

358

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“…In particular, this method played the role of a benchmark numerical experiment when developing the multicentre-basis Hartree-Fock approach [20] as well as the quasiclassical theory further discussed in Section 8. Figure 6 shows a typical result obtained by means of an exact-diagonalization study: the ground-state phase diagram of a six-electron parabolic quantum dot placed into a perpendicular magnetic field.…”

Section: Angular Momentum Transitionsmentioning

confidence: 99%

“…In particular, standard methods of atomic and molecular physics -such as the Hartree, Hartree-Fock, and density functional theory -have been extensively exploited [1,[20][21][22][23]. At high electron densities the physics is dominated by quantum degeneracy, and the interparticle interaction acts a rather weak correction.…”

Section: Introductionmentioning

confidence: 99%

Quasiclassical theory of quantum dots

Anisimovas¹,

Matulis²

2010

Lithuanian J. Phys.

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We review the quasiclassical theory of quantum dots. The starting point of the developed approximate approaches is the observation that in large (in comparison to the effective Bohr radius) quantum dots the energy of the classical Coulomb interactions dominates over the quantum-mechanical kinetic energy. This dominance is further enhanced by application of a perpendicular magnetic field. The classical regime is marked by the formation of structures (the Wigner crystal) and structural transitions. The nature of these phenomena is indeed classical, and they can be successfully tackled using classical approaches which are transparent and easy to understand. In this way heavy calculations typical of quantum-mechanical schemes are avoided and the quantum effects are included in an perturbative manner. We discus, in particular, the application of the renormalized perturbation series to the energy spectra, the structural transitions, the power law behaviour of the critical fields, the global (persistent) and local currents in quantum dots, and dissipation in mixed systems with both quantum and classical degerees of freedom.

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Hartree–Fock energy of a finite two-dimensional electron gas system in a jellium background

Ciftja

2015

Physica B: Condensed Matter

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Accuracy of the Hartree-Fock method for Wigner molecules at high magnetic fields

Cited by 14 publications

References 42 publications

Symmetry breaking and quantum correlations in finite systems: studies of quantum dots and ultracold Bose gases and related nuclear and chemical methods

Symmetry breaking and quantum correlations in finite systems: studies of quantum dots and ultracold Bose gases and related nuclear and chemical methods

Quasiclassical theory of quantum dots

Hartree–Fock energy of a finite two-dimensional electron gas system in a jellium background

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