Anharmonic Contribution to the Energy of a Dilute Electron Gas—Interpolation for the Correlation Energy

Carr, W. J.; Coldwell-Horsfall, Rosemary A.; Fein, A. E.

doi:10.1103/physrev.124.747

Cited by 142 publications

(40 citation statements)

References 12 publications

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“…(1) in powers of 1/r 1/2 s . 24,25 The leading term, proportional to 1/r s , corresponds to the Madelung energy E M of Eq.(2). In free space, it attains its minimum value E BCC = −0.89593/r s (in atomic units) for a Body Centered Cubic (BCC) Wigner crystal.…”

Section: Wigner Crystallization In Layered Solids a Model And Apmentioning

confidence: 99%

Enhancement of Wigner crystallization in quasi-low-dimensional solids

Rastelli¹,

Quemerais²,

Fratini³

2006

Phys. Rev. B

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The crystallization of electrons in quasi low-dimensional solids is studied in a model which retains the full three-dimensional nature of the Coulomb interactions. We show that restricting the electron motion to layers (or chains) gives rise to a rich sequence of structural transitions upon varying the particle density. In addition, the concurrence of low-dimensional electron motion and isotropic Coulomb interactions leads to a sizeable stabilization of the Wigner crystal, which could be one of the mechanisms at the origin of the charge ordered phases frequently observed in such compounds.

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Section: Wigner Crystallization In Layered Solids a Model And Apmentioning

confidence: 99%

Enhancement of Wigner crystallization in quasi-low-dimensional solids

Rastelli¹,

Quemerais²,

Fratini³

2006

Phys. Rev. B

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“…The up-pointing triangles show the Ceperley-Alder results for the BCC crystal; the dashed-dashed-dotted line is a fit to this data. Finally, the dashed-dotted line shows the prediction of the phonon model of Carr et al 21 Where error bars on the DMC data cannot be seen, it is because they are smaller than the symbols showing the data points.…”

Section: Locating the Fluid-to-crystal Transition Densitymentioning

confidence: 99%

Diffusion quantum Monte Carlo study of three-dimensional Wigner crystals

et al. 2004

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We report diffusion quantum Monte Carlo calculations of three-dimensional Wigner crystals in the density range rs = 100 to 150. We have tested different types of orbital for use in the approximate wave functions but none improve upon the simple Gaussian form. The Gaussian exponents are optimized by directly minimizing the diffusion quantum Monte Carlo energy. We have carefully investigated and sought to minimize the potential biases in our Monte Carlo results. We conclude that the uniform electron gas undergoes a transition from a ferromagnetic fluid to a body-centered cubic Wigner crystal at rs = 106±1. The diffusion quantum Monte Carlo results are compared with those from Hartree-Fock and Hartree theory in order to understand the role played by exchange and correlation in Wigner crystals. We also study "floating" Wigner crystals and give results for their pair correlation functions.

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“…67 The next term, +2.65/r 3/2 s ryd, describes the coupled harmonic zerotemperature motion in lowest order . 68,69,70 To estimate the corresponding n(k, r s ), we define with 3 ω/2 = 2.65/r …”

Section: Appendix B: the Momentum Distribution Of The Wigner Crystalmentioning

confidence: 99%

Momentum distribution of the uniform electron gas: Improved parametrization and exact limits of the cumulant expansion

2002

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The momentum distribution of the unpolarized uniform electron gas in its Fermi-liquid regime, n(k, rs), with the momenta k measured in units of the Fermi wave number kF and with the density parameter rs, is constructed with the help of the convex Kulik function G(x). It is assumed that n(0, rs), n(1 ± , rs), the on-top pair density g(0, rs) and the kinetic energy t(rs) are known (respectively, from accurate calculations for rs = 1, ..., 5, from the solution of the Overhauser model, and from Quantum Monte Carlo calculations via the virial theorem). Information from the high-and the low-density limit, corresponding to the random-phase approximation and to the Wigner crystal limit, is used. The result is an accurate parametrization of n(k, rs), which fulfills most of the known exact constraints. It is in agreement with the effective-potential calculations of Takada and Yasuhara [Phys. Rev. B 44, 7879 (1991)], is compatible with Quantum Monte Carlo data, and is valid in the density range rs 12. The corresponding cumulant expansions of the pair density and of the static structure factor are discussed, and some exact limits are derived.

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Anharmonic Contribution to the Energy of a Dilute Electron Gas—Interpolation for the Correlation Energy

Cited by 142 publications

References 12 publications

Enhancement of Wigner crystallization in quasi-low-dimensional solids

Enhancement of Wigner crystallization in quasi-low-dimensional solids

Diffusion quantum Monte Carlo study of three-dimensional Wigner crystals

Momentum distribution of the uniform electron gas: Improved parametrization and exact limits of the cumulant expansion

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