Spin-dependent correlations and thermodynamic functions for electron liquids at arbitrary degeneracy and spin polarization

Tanaka, Shigenori; Ichimaru, Setsuo

doi:10.1103/physrevb.39.1036

Cited by 61 publications

(100 citation statements)

References 56 publications

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“…Tanaka and Ichimaru 23 have computed the polarization phase diagram of the electron gas both at zero and non-zero temperature using an integral equation method. At zero temperature they obtain a result similar to Ortiz at al.…”

Section: The Phase Diagrammentioning

confidence: 99%

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

2002

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To determine the state of spin polarization of the 3D electron gas at very low densities and zero temperature, we calculate the energy versus spin polarization using Diffusion Quantum Monte Carlo methods with backflow wavefunctions and twist averaged boundary conditions. We find a second order phase transition to a partially polarized phase at rs ∼ 50 ± 2. The magnetic transition temperature is estimated using an effective mean field method, the Stoner model.

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Section: The Phase Diagrammentioning

confidence: 99%

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

2002

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“…A Padé approximant as originally given by Ichimaru et al [22,[26][27][28] and also employed in Ref. 18 for u ee is suggestive.…”

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confidence: 99%

Accurate Homogeneous Electron Gas Exchange-Correlation Free Energy for Local Spin-Density Calculations

et al. 2014

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An accurate analytical parametrization for the exchange-correlation free energy of the homogeneous electron gas, including interpolation for partial spin-polarization, is derived via thermodynamic analysis of recent restricted path integral Monte-Carlo (RPIMC) data. This parametrization constitutes the local spin density approximation (LSDA) for the exchange-correlation functional in density functional theory. The new finite-temperature LSDA reproduces the RPIMC data well, satisfies the correct high-density and low-and high-T asymptotic limits, and is well-behaved beyond the range of the RPIMC data, suggestive of broad utility. PACS numbers:The homogeneous electron gas (HEG) is a fundamentally important system for understanding many-fermion physics. In the absence of exact analytical solutions for its energetics, high-precision numerical results have been critical to insight. Recently published [1] restricted path integral Monte Carlo (RPIMC) data for the HEG over a wide range of temperatures and densities open the opportunity to obtain closed form expressions for HEG thermodynamics, in particular the exchange and correlation (XC) contributions. Such expressions extracted from Monte Carlo data are well-known for the zero-T HEG, where they have played a major role in understanding inhomogeneous electron-system behavior. We provide the corresponding thermodynamical expressions for wide temperature and density ranges.Density functional theory (DFT) is the motivating context. For ground-state DFT, the most basic exchangecorrelation (XC) density functional is the local density approximation (LDA). It approximates the local XC energy per particle, ε xc , as the value for the HEG at the local density, ε LDA xc (n(r)) ≈ ε HEG xc (n)| n=n(r) [also see Eq. (3) [5] for the spin-polarized T = 0 K HEG also validate the spininterpolation formulae used in that case, the local spin density approximation (LSDA). All more refined ε xc approximations reduce to the LSDA in the weak inhomogeneity limit.Finite-temperature DFT [6-8] increasingly is being used to study matter under diverse density and temperature conditions [9][10][11][12][13][14]. In it, the XC free-energy is defined by decomposition of the universal free-energy density functional (independent of the external potential). With the T -dependence suppressed for now, that functional isThe first two terms are the non-interacting kinetic energy and entropy (also known as the Kohn-Sham KE and entropy), F H [n] is the classical electron-electron Coulomb energy, and the XC free energy by definition iswith T [n] and S[n] the interacting system kinetic energy and entropy and U ee [n] the full quantum mechanical electron-electron interaction energy. Just as for T = 0 K, the existence theorems of finite-T DFT are not constructive for F xc , so approximations must be devised. Common practice [9] in simulations is to use a. This gives only the implicit T -dependence provided by n(r, T ). However, there is substantial evidence from both finite-T Hartree-Fock [12,15] and finite-T exac...

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“…This is precisely what our numerical calculations, based on the formulas of Ref. 18, indicate. As we shall see, this result is important in understanding the behavior of the diffusion constant of a unipolar spin packet when the system is fully spin polarized.…”

Section: B Low-temperature Limitmentioning

confidence: 57%

“…We evaluated S numerically starting from the formulas provided by Tanaka and Ichimaru, 18 who calculated the freeenergy density of the three-dimensional electron gas as a function of temperature, density, and spin polarization. Figure 4 shows S divided by its noninteracting value S ni as a function of the dimensionless temperature T/T F for various densities, starting with nϭ4.2ϫ10 17 cm Ϫ3 for the upper curve ͑labeled n h ) down to nϭ4.2ϫ10 11 cm Ϫ3 for the lowest one ͑labeled n l ), decreasing by two orders of magnitude from one curve to the next.…”

Section: Spin Stiffness Of An Interacting Spin-polarized Electronmentioning

confidence: 99%

Coulomb interaction effects in spin-polarized transport

D’Amico

Vignale

2002

Phys. Rev. B

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We study the effect of the electron-electron interaction on the transport of spin-polarized currents in metals and doped semiconductors in the diffusive regime. In addition to well-known screening effects, we identify two additional effects, which depend on many-body correlations and exchange and reduce the spin-diffusion constant. The first is the ''spin Coulomb drag''-an intrinsic friction mechanism which operates whenever the average velocities of up-spin and down-spin electrons differ. The second arises from the decrease in the longitudinal spin stiffness of an interacting electron gas relative to a noninteracting one. Both effects are studied in detail for both degenerate and nondegenerate carriers in metals and semiconductors, and various limiting cases are worked out analytically. The behavior of the spin-diffusion constant at and below a ferromagnetic transition temperature is also discussed.

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Spin-dependent correlations and thermodynamic functions for electron liquids at arbitrary degeneracy and spin polarization

Cited by 61 publications

References 56 publications

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

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

Accurate Homogeneous Electron Gas Exchange-Correlation Free Energy for Local Spin-Density Calculations

Coulomb interaction effects in spin-polarized transport

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