Zero Temperature Phases of the Electron Gas

Ortíz, Gerardo; Harris, Michael L.; Ballone, Pietro

doi:10.1103/physrevlett.82.5317

Cited by 271 publications

(291 citation statements)

References 16 publications

(31 reference statements)

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“…The problem of self-consistency in GW calculations has been investigated more deeply in such simple systems as the homogeneous electron gas or an exactly solvable Hubbard model. The main outcome of the self-consistent GW calculation for the homogeneous electron gas (Holm and von Barth, 1998;Holm and Aryasetiawan, 2000;García-Gonzá lez and Godby, 2001) is that the total energy computed with the Galitskii and Migdal (1958) formula turns out to be strikingly close to the total energy calculated using quantum Monte Carlo (Ceperley and Alder, 1980;Ortiz et al, 1999). Here few sum rules already determine most of the energy contributions in the homogeneous electron gas.…”

Section: First Iteration Step: the Gw Approximationmentioning

confidence: 99%

“…The simplest approximation (still widely used) to E xc is the local-density approximation (Kohn and Sham, 1965). The approximation is based on using the exchange-correlation energy density ⑀ xc hom of the homogeneous electron gas (Ceperley and Alder, 1980;Ortiz et al, 1999), namely, E xc LDA ͓ ͔ϭ͐⑀ xc hom " (r)… (r)dr. Hence one replaces the inhomogeneous electron system at each point r by a homogeneous electron gas having the density of the inhomogeneous system at r. The rationale for this approximation is in the limit of slowly varying density.…”

Section: Ksmentioning

confidence: 99%

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Electronic excitations: density-functional versus many-body Green’s-function approaches

2002

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Electronic excitations lie at the origin of most of the commonly measured spectra. However, the first-principles computation of excited states requires a larger effort than ground-state calculations, which can be very efficiently carried out within density-functional theory. On the other hand, two theoretical and computational tools have come to prominence for the description of electronic excitations. One of them, many-body perturbation theory, is based on a set of Green's-function equations, starting with a one-electron propagator and considering the electron-hole Green's function for the response. Key ingredients are the electron's self-energy ⌺ and the electron-hole interaction. A good approximation for ⌺ is obtained with Hedin's GW approach, using density-functional theory as a zero-order solution. First-principles GW calculations for real systems have been successfully carried out since the 1980s. Similarly, the electron-hole interaction is well described by the Bethe-Salpeter equation, via a functional derivative of ⌺. An alternative approach to calculating electronic excitations is the time-dependent density-functional theory (TDDFT), which offers the important practical advantage of a dependence on density rather than on multivariable Green's functions. This approach leads to a screening equation similar to the Bethe-Salpeter one, but with a two-point, rather than a four-point, interaction kernel. At present, the simple adiabatic local-density approximation has given promising results for finite systems, but has significant deficiencies in the description of absorption spectra in solids, leading to wrong excitation energies, the absence of bound excitonic states, and appreciable distortions of the spectral line shapes. The search for improved TDDFT potentials and kernels is hence a subject of increasing interest. It can be addressed within the framework of many-body perturbation theory: in fact, both the Green's functions and the TDDFT approaches profit from mutual insight. This review compares the theoretical and practical aspects of the two approaches and their specific numerical implementations, and presents an overview of accomplishments and work in progress. CONTENTS

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Section: First Iteration Step: the Gw Approximationmentioning

confidence: 99%

Section: Ksmentioning

confidence: 99%

Electronic excitations: density-functional versus many-body Green’s-function approaches

2002

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“…Specific symmetries for the fully correlated uniform electron gas have been investigated using Monte Carlo methods. 2,3 These studies focus mostly on broken spatial symmetry, i.e., Wigner crystallization or broken global spin symmetry.…”

Section: Introductionmentioning

confidence: 99%

Noncollinear spin-spiral phase for the uniform electron gas within reduced-density-matrix-functional theory

et al. 2010

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The noncollinear spin-spiral density wave of the uniform electron gas is studied in the framework of reduced-density-matrix-functional theory. For the Hartree-Fock approximation, which can be obtained as a limiting case of reduced-density-matrix-functional theory, Overhauser showed a long-time ago that the paramagnetic state of the electron gas is unstable with respect to the formation of charge-or spin-density waves. Here we not only present a detailed numerical investigation of the spin-spiral density wave in the Hartree-Fock approximation but also investigate the effects of correlations on the spin-spiral density wave instability by means of a recently proposed density-matrix functional.

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“…an unconventional state in the parent, CaB 6 , [4,5,6,7] and the second was based on the ferromagnetic phase of the dilute electron gas. [1, 8,9] In the first class, the ferromagnetism arises from La induced doping of carriers into an excitonic ground state. This depends on a bare band structure that is semimetallic or very close to it, so that the prerequisite instability of CaB 6 to an excitonic state can exist.…”

mentioning

confidence: 99%

Electronic structure of calcium hexaboride within the weighted density approximation

Singh

Cohen

2004

Phys. Rev. B

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We report calculations of the electronic structure of CaB 6 using the weighted density approximation (WDA) to density functional theory. We find a semiconducting band structure with a sizable gap, in contrast to local density approximation (LDA) results, but in accord with recent experimental data. In particular, we find an X-point band gap of 0.8 eV. The WDA correction of the LDA error in describing the electronic structure of CaB 6 is discussed in terms of the orbital character of the bands and the better cancelation of self-interactions within the WDA.

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Zero Temperature Phases of the Electron Gas

Cited by 271 publications

References 16 publications

Electronic excitations: density-functional versus many-body Green’s-function approaches

Electronic excitations: density-functional versus many-body Green’s-function approaches

Noncollinear spin-spiral phase for the uniform electron gas within reduced-density-matrix-functional theory

Electronic structure of calcium hexaboride within the weighted density approximation

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