Fixed-phase quantum Monte Carlo method applied to interacting electrons in a quantum dot

Bolton, F.

doi:10.1103/physrevb.54.4780

Cited by 68 publications

(71 citation statements)

References 28 publications

(24 reference statements)

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“…If instead we choose to employ states with definite L then the wave functions are complex, and we must use the fixed-phase approximation, 55,56 the generalization of the fixed-node method to complex wave functions. Usually the fixed-phase error is comparable to and slightly larger than the fixed-node error.…”

Section: Methodsmentioning

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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Section: Methodsmentioning

confidence: 99%

Incipient Wigner localization in circular quantum dots

et al. 2007

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“…QMC techniques have also been used for 2D (Bolton, 1996;Egger et al, 1999;Harju et al, 1999;Pederiva, Umrigar, and Lipparini, 2000) as well as 3D structures (Taut, 1993;Thompson and Alavi, 2002;Cioslowski and Buchowiecki, 2005;Cioslowski and Pernal, 2006;Ryabinkin and Staroverov, 2010). The two-electron problem in a harmonic-oscillator potential in 3D is analytically solvable for certain harmonicoscillator frequencies (Taut, 1993) making it an ideal test ground to study the Coulomb correlation.…”

Section: D and 3d Quantum Dots And Quantum Wellsmentioning

confidence: 99%

Theory and application of explicitly correlated Gaussians

et al. 2013

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The variational method complemented with the use of explicitly correlated Gaussian basis functions is one of the most powerful approaches currently used for calculating the properties of few-body systems. Despite its conceptual simplicity, the method offers great flexibility, high accuracy, and can be used to study diverse quantum systems, ranging from small atoms and molecules to light nuclei, hadrons, quantum dots, and Efimov systems. The basic theoretical foundations are discussed, recent advances in the applications of explicitly correlated Gaussians in physics and chemistry are reviewed, and the strengths and weaknesses of the explicitly correlated Gaussians approach are compared with other few-body techniques.

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“…Not only does it provide benchmark results for the ground state energy and wave function, but also it gives access to excited states and hence permits an interpretation of a number of spectroscopic techniques such as far-infrared [11], photoluminescence [14], and Raman [15]. In contrast, the quantum Monte Carlo (QMC) [26,27,28,29,30,31,32,33,34], mean-field Hartree-Fock [35,36], and density-functional theory (DFT) calculations [37,38,39,40,41,42] are restricted to the ground-state properties.…”

Section: Introductionmentioning

confidence: 99%