The self-energy of the uniform electron gas in the second order of exchange

Ziesche, P.

doi:10.1002/andp.200610220

Cited by 11 publications

(9 citation statements)

References 13 publications

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“…[13][14][15][16] Local orbitals, [17][18][19][20] local interactions, 1,[21][22][23][24] and length scale (including range separation) schemes 22,25,26 have also been developed that exploit a length scale separation between correlations within a unit cell and correlations between unit cells. Finally, some many-body methods can be directly integrated to find the thermodynamic limit [27][28][29][30][31][32][33] from which analytic corrections can be derived. 34 Even for a finite system, a finite number of basis functions yields a different type of finite size effect in wavefunction calculations.…”

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confidence: 99%

Communication: Convergence of many-body wave-function expansions using a plane-wave basis in the thermodynamic limit

Shepherd

2016

The Journal of Chemical Physics

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Basis set incompleteness error and finite size error can manifest concurrently in systems for which the two effects are phenomenologically well-separated in length scale. When this is true, we need not necessarily remove the two sources of error simultaneously. Instead, the errors can be found and remedied in different parts of the basis set. This would be of great benefit to a method such as coupled cluster theory since the combined cost of n 6 occ n 4 virt could be separated into n 6 occ and n 4 virt costs with smaller prefactors. In this Communication, we present analysis on a data set due to Baardsen and coworkers, containing coupled cluster doubles energies for the 2DEG for r s = 0.5, 1.0 and 2.0 a.u. at a wide range of basis set sizes and particle numbers. In obtaining complete basis set limit thermodynamic limit results, we find that within a small and removable error the above assertion is correct for this simple system. This approach allows for the combination of methods which separately address finite size effects and basis set incompleteness error.

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confidence: 99%

Communication: Convergence of many-body wave-function expansions using a plane-wave basis in the thermodynamic limit

Shepherd

2016

The Journal of Chemical Physics

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“…that is known due to the calculations of Glasser and Lamb [65] and Ziesche [16] or from the second-order correction to the total energy computed by Onsager et al [66]. According to the Hugenholtz-van Hove-Luttinger-Ward theorem they are equal.…”

Section: B 2x Results For 3d Hegmentioning

confidence: 98%

“…electron gas [16]. Third, the mechanism with screening has been considered in the calculations of quasiparticle lifetimes.…”

Section: Introductionmentioning

confidence: 99%

Dynamically screened vertex correction to GW

2020

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Diagrammatic perturbation theory is a powerful tool for the investigation of interacting many-body systems, the self-energy operator encoding all the variety of scattering processes. In the simplest scenario of correlated electrons described by the GW approximation for the electron self-energy, a particle transfers a part of its energy to neutral excitations. Higher-order (in screened Coulomb interaction W ) self-energy diagrams lead to improved electron spectral functions (SFs) by taking more complicated scattering channels into account and by adding corrections to lower order self-energy terms. However, they also may lead to unphysical negative spectral functions. The resolution of this difficulty has been demonstrated in our previous works. The main idea is to represent the self-energy operator in a Fermi golden rule form which leads to a manifestly positive definite SF and allows for a very efficient numerical algorithm. So far, the method has only been applied to the three-dimensional electron gas, which is a paradigmatic system, but a rather simple one. Here we systematically extend the method to two dimensions including realistic systems such as monolayer and bilayer graphene. We focus on one of the most important vertex function effects involving the exchange of two particles in the final state. We demonstrate that it should be evaluated with the proper screening and discuss its influence on the quasiparticle properties.

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“…As a result, he showed the subtle cancellation of contributions from self-energy and vertex-corrections to spectral properties of charged particles, exemplified for the damping of plasmons in Al. Very recently, Ziesche [49] has reviewed the calculation of direct and exchange contributions (vertex correction) to the on-shell self-energy of the homogenous electron-gas.…”

Section: Applications Of Gw γ-Approximation For the Self-energymentioning

confidence: 99%

Optical Properties and One‐Particle Spectral Function in Non‐Ideal Plasmas

Fortmann

Röpke

Wierling

2007

Contrib. Plasma Phys.

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A basic concept to calculate physical features of non-ideal plasmas, such as optical properties, is the spectral function which is linked to the self-energy. We calculate the spectral function for a non-relativistic hydrogen plasma in GW -approximation. In order to go beyond GW approximation, we include self-energy and vertex correction to the polarization function in lowest order. Partial compensation is observed. The relation of our approach to GW and GW Γ calculations in other fields, such as the band-structure calculations in semiconductor physics, is discussed. From the spectral function we derive the absorption coefficient due to inverse bremsstrahlung via the polarization function. As a result, a significant reduction of the absorption as compared to the Bethe-Heitler formula for bremsstrahlung is obtained.

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The self-energy of the uniform electron gas in the second order of exchange

Cited by 11 publications

References 13 publications

Communication: Convergence of many-body wave-function expansions using a plane-wave basis in the thermodynamic limit

Communication: Convergence of many-body wave-function expansions using a plane-wave basis in the thermodynamic limit

Dynamically screened vertex correction to GW

Optical Properties and One‐Particle Spectral Function in Non‐Ideal Plasmas

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