Erratum: Diffusion Monte Carlo study of circular quantum dots [Phys. Rev. B 62, 8120 (2000)]

Pederiva, Francesco; Umrigar, C. J.; Lipparini, E.

doi:10.1103/physrevb.68.089901

Cited by 30 publications

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“…The energy for low-lying excitations becomes very small in the low density limit (strong electron correlations), and, therefore, the constraint on the temperature becomes extremely stringent. DMC provides quite reliable results [395][396][397][398]. It contains some systematic "fixed-mode" error which are, however, smaller than the systematic and statistical errors of PIMC.…”

Section: Theoretical Approachesmentioning

confidence: 96%

Effects of symmetry breaking in finite quantum systems

2013

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The review considers the peculiarities of symmetry breaking and symmetry transformations and the related physical effects in finite quantum systems. Some types of symmetry in finite systems can be broken only asymptotically. However, with a sufficiently large number of particles, crossover transitions become sharp, so that symmetry breaking happens similarly to that in macroscopic systems. This concerns, in particular, global gauge symmetry breaking, related to Bose-Einstein condensation and superconductivity, or isotropy breaking, related to the generation of quantum vortices, and the stratification in multicomponent mixtures. A special type of symmetry transformation, characteristic only for finite systems, is the change of shape symmetry. These phenomena are illustrated by the examples of several typical mesoscopic systems, such as trapped atoms, quantum dots, atomic nuclei, and metallic grains. The specific features of the review are: (i) the emphasis on the peculiarities of the symmetry breaking in finite mesoscopic systems; (ii) the analysis of common properties of physically different finite quantum systems; (iii) the manifestations of symmetry breaking in the spectra of collective excitations in finite quantum systems. The analysis of these features allows for the better understanding of the intimate relation between the type of symmetry and other physical properties of quantum systems. This also makes it possible to predict new effects by employing the analogies between finite quantum systems of different physical nature.

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Section: Theoretical Approachesmentioning

confidence: 96%

Effects of symmetry breaking in finite quantum systems

2013

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“…Although PIMC treats interactions accurately, it has its own systematic and statistical problems; for instance, it generates a thermal average of states with different L and S quantum numbers, only preserving S z symmetry. To avoid these various difficulties and to clarify the scenario, we have carried out a study using the variational Monte Carlo (VMC) and diffusion Monte Carlo (DMC) techniques 9 , which we used previously to study both circular [20][21][22] and irregular 23 dots at r s ∼ 2. This method is free of the problems of PIMC but is approximate in that a 'fixed-node' error is made.…”

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confidence: 99%

Correlation-induced inhomogeneity in circular quantum dots

et al. 2006

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Properties of the 'electron gas'-in which conduction electrons interact by means of Coulomb forces but ionic potentials are neglected-change dramatically depending on the balance between kinetic energy and Coulomb repulsion. The limits are well understood 1 . For very weak interactions (high density), the system behaves as a Fermi liquid, with delocalized electrons. In contrast, in the strongly interacting limit (low density), the electrons localize and order into a Wigner crystal phase. The physics at intermediate densities, however, remains a subject of fundamental research 2-8 . Here, we study the intermediate-density electron gas confined to a circular disc, where the degree of confinement can be tuned to control the density. Using accurate quantum Monte Carlo techniques 9 , we show that the electron-electron correlation induced by an increase of the interaction first smoothly causes rings, and then angular modulation, without any signature of a sharp transition in this density range. This suggests that inhomogeneities in a confined system, which exist even without interactions, are significantly enhanced by correlations.Quantum dots 10 -a nanoscale island containing a puddle of electrons-provide a highly tunable and simple setting to study the effects of large Coulomb interaction. They introduce level quantization and quantum interference in a controlled way, and can, in principle, be made in the very-low-density regime, where correlation effects are strong 11 . In addition, there are natural parallels between quantum dots and other confined systems of interacting particles, such as cold atoms in traps.Therefore, we consider a model quantum dot consisting of electrons moving in a two-dimensional (2D) plane, with kinetic energy (−(1/2) i ∇ with n being the density of electrons. For our confined system in which n(r) varies, we define r s in the same way using the mean densityn ≡ n 2 (r)dr/N. We have studied this system up to N = 20 electrons. The spring constant ω makes the oscillator potential narrow (for large ω) or shallow (for small ω); it thereby tunes the average density of electrons between high and low values, thus controlling r s . For example, for N = 20, varying ω between 3 and 0.0075 changes r s from 0.4 to 17.7. The radius of the dot grows significantly as r s increases, in an approximately linear fashion (see Fig. 1).In the bulk 2D electron gas, numerical work suggests a transition from a Fermi-liquid state to a Wigner crystal around r c s ≈ 30-35 (refs 2-4,8). On the other hand, experiments on the 2D electron gas (which include, of course, disorder and residual effects of the ions) show more-complex behaviour, including evidence for a metal-insulator transition 5 . Circular quantum dots have been studied previously using a variety of methods, yielding a largely inconclusive scenario. Many studies 12-14 have used density functional theory or the HartreeFock method. These typically predict charge or spin-density-wave order even for modest r s (unless the symmetry is restored after the fact 14 ), ...

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“…This has been carried out in a number of cases for high to medium density quantum dots. 43,44,45,46,47 We discuss this method in more detail below. Briefly, while there is a systematic "fixed-node error", it is considerably smaller than the systematic and statistical errors of PIMC.…”

Section: Introductionmentioning

confidence: 99%

Incipient Wigner localization in circular quantum dots

et al. 2007

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We study the development of electron-electron correlations in circular quantum dots as the density is decreased. We consider a wide range of both electron number, N ≤ 20, and electron gas parameter, rs < ∼ 18, using the diffusion quantum Monte Carlo technique. Features associated with correlation appear to develop very differently in quantum dots than in bulk. The main reason is that translational symmetry is necessarily broken in a dot, leading to density modulation and inhomogeneity. Electron-electron interactions act to enhance this modulation ultimately leading to localization. This process appears to be completely smooth and occurs over a wide range of density. Thus there is a broad regime of "incipient" Wigner crystallization in these quantum dots. Our specific conclusions are: (i) The density develops sharp rings while the pair density shows both radial and angular inhomogeneity. (ii) The spin of the ground state is consistent with Hund's (first) rule throughout our entire range of rs for all 4 ≤ N ≤ 20. (iii) The addition energy curve first becomes smoother as interactions strengthen -the mesoscopic fluctuations are damped by correlation -and then starts to show features characteristic of the classical addition energy. (iv) Localization effects are stronger for a smaller number of electrons. (v) Finally, the gap to certain spin excitations becomes small at the strong interaction (large rs) side of our regime.

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Erratum: Diffusion Monte Carlo study of circular quantum dots [Phys. Rev. B 62, 8120 (2000)]

Cited by 30 publications

References 0 publications

Effects of symmetry breaking in finite quantum systems

Effects of symmetry breaking in finite quantum systems

Correlation-induced inhomogeneity in circular quantum dots

Incipient Wigner localization in circular quantum dots

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