Spin polarization of the low-density three-dimensional electron gas

Zong, Fenghua; Lin, Chao-Ping; Ceperley, David M.

doi:10.1103/physreve.66.036703

Cited by 124 publications

(172 citation statements)

References 24 publications

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“…The statistical error bars on their data are much larger than on the fluid data of Zong et al 6 or on our Wigner crystal data, which hampers detailed comparisons. However, it appears that the main reason for the discrepancy is that Ortiz to highlight the differences between phases.…”

Section: Locating the Fluid-to-crystal Transition Densitymentioning

confidence: 65%

“…We found the transition from the fluid to crystalline phases to occur at r s = 106 ± 1, in agreement with the original result of Ceperley and Alder. 3 Note, however, that the transition density predicted using the fluid data of Zong et al 6 in conjunction with the crystal data of Ceperley and Alder would be somewhat lower, at about r s = 127. Our Wigner crystal energies are slightly lower than those of Ceperley and Alder, even though they studied a Bose crystal, which must have a lower energy than the corresponding fermion one.…”

Section: Locating the Fluid-to-crystal Transition Densitymentioning

confidence: 95%

“…We make use of the highly accurate DMC energies of Zong et al 6 for the ferromagnetic fluid phase at low densities, which used trial wave functions including "backflow" effects. We found an excellent fit to Eq.…”

Section: Locating the Fluid-to-crystal Transition Densitymentioning

confidence: 99%

“…In their pioneering DMC study of the phases of the electron gas, Ceperley and Alder 3 obtained a transition density of r s = 100 ± 20, 4 but a more recent DMC study gave r s = 65 ± 10. 5 Moreover, highly accurate DMC energies for the low-density fluid have recently become available 6 , which may further modify predictions of the transition density. The primary goal of this work is to provide highly accurate DMC energies for three-dimensional Wigner crystals and to use them in conjunction with the fluid data of Zong et al 6 to predict an accurate value for the transition density.…”

Section: Introductionmentioning

confidence: 99%

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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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Section: Locating the Fluid-to-crystal Transition Densitymentioning

confidence: 65%

Section: Locating the Fluid-to-crystal Transition Densitymentioning

confidence: 95%

Section: Locating the Fluid-to-crystal Transition Densitymentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Diffusion quantum Monte Carlo study of three-dimensional Wigner crystals

et al. 2004

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“…23,24 The resulting bias is negative, and is generally believed to fall off as 1/N , where N is the number of atoms in the simulation cell. 11,25,26,27 In order to eliminate the finite-size bias, simulations were carried out in supercells consisting of 3×3×3 and 4×4×4 primitive unit cells. The error in the DFT results arising from the use of a 3 × 3 × 3 k-point mesh is small (about 0.0001 a.u.…”

Section: Finite-size Biasmentioning

confidence: 99%

Quantum Monte Carlo, density functional theory, and pair potential studies of solid neon

Drummond

Needs

2006

Phys. Rev. B

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We report quantum Monte Carlo (QMC), plane-wave density-functional theory (DFT), and interatomic pair-potential calculations of the zero-temperature equation of state (EOS) of solid neon. We find that the DFT EOS depends strongly on the choice of exchange-correlation functional, whereas the QMC EOS is extremely close to both the experimental EOS and the EOS obtained using the best semiempirical pair potential in the literature. This suggests that QMC is able to give an accurate treatment of van der Waals forces in real materials, unlike DFT. We calculate the QMC EOS up to very high densities, beyond the range of values for which experimental data are currently available. At high densities the QMC EOS is more accurate than the pair-potential EOS. We generate a different pair potential for neon by a direct evaluation of the QMC energy as a function of the separation of an isolated pair of neon atoms. The resulting pair potential reproduces the EOS more accurately than the equivalent potential generated using the coupled-cluster CCSD(T) method.

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On the crystalline states of the dilute jellium model

Ciccariello¹

2009

Ann. Phys.

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Strongly localized quantum crystalline states (SLQCS) are determinantal wave-functions made up of the single-particle wave-functions that are obtained from all the distinct crystalline translations of a particular wave-function different from zero only within a primitive cell of the considered crystal and dependent on some parameters α1, . . . , αn. The expectation value of the Hamiltonian of the jellium model is numerically evaluated over a class of SLQCS depending on a single parameter α. The minimization of this value with respect to α yields an energy smaller than that of the polarized jellium fluid. The results, compared with the more accurate results obtained by Hartree-Fock and quantum Monte-Carlo procedures, further clarify the importance of the electron localization for the transition to a crystalline phase as well as the localization increase with decreasing density.

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Spin polarization of the low-density three-dimensional electron gas

Cited by 124 publications

References 24 publications

Diffusion quantum Monte Carlo study of three-dimensional Wigner crystals

Diffusion quantum Monte Carlo study of three-dimensional Wigner crystals

Quantum Monte Carlo, density functional theory, and pair potential studies of solid neon

On the crystalline states of the dilute jellium model

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