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Model Vertices Beyond the GW Approximation

Hindgren, Mikael LU (1997)
Abstract
We study the effects of local vertex corrections to the self energy of the electron gas. We find that a vertex derived from time-dependent density-functional theory can give accurate self energies without including the explicit time dependence of the exchange-correlation potential provided, however, that a proper decay at large momentum transfer (large q) is built into the vertex function. (The local-density approximation for the vertex fails badly.) Total energies are calculated from the Galitskii-Migdal formula and it is shown that a proper large-q behavior, results in a close consistency between the chemical potentials derived from these energies and those obtained directly from the self energy. We show that this internal consistency... (More)
We study the effects of local vertex corrections to the self energy of the electron gas. We find that a vertex derived from time-dependent density-functional theory can give accurate self energies without including the explicit time dependence of the exchange-correlation potential provided, however, that a proper decay at large momentum transfer (large q) is built into the vertex function. (The local-density approximation for the vertex fails badly.) Total energies are calculated from the Galitskii-Migdal formula and it is shown that a proper large-q behavior, results in a close consistency between the chemical potentials derived from these energies and those obtained directly from the self energy. We show that this internal consistency depends critically on including the same vertex correction in both the self-energy and the screening function. In addition the total energies become almost as accurate as those from elaborate quantum Monte-Carlo (QMC) calculations.



We also study the accuracy and utility of the functional for the total energy proposed by Luttinger and Ward and a generalization by Almbladh, von Barth, and van Leeuwen. For the electron gas, even the simplest and readily evaluated approximations to these functionals yield total energies of similar quality as those of QMC calculations. The functionals depend on the one-electron Green's function and the screened Coulomb interaction and already rather crude approximations to these quantities produce accurate energies thus demonstrating the insensitivity of the functionals to their arguments.



Different ways of incorporating vertex corrections beyond the $GW$ level are studied in simple, exactly soluble polaron-like models. We study models of a structureless core electron coupled to valence electrons and a local polaron model by Cini, Hewson and Newns. Our model results indicate that the first vertex correction alone will in general not suffice to improve the spectrum away from the quasi-particle peak. By including a subsequence of Mahan's fractal vertex series, however, we obtain results with correct physical properties which agree better with exact model results. (Less)
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author
opponent
  • Prof Rajagopal, A. K., Naval Research Lab., Washington D.C., USA
organization
publishing date
type
Thesis
publication status
published
subject
keywords
Matematisk och allmän teoretisk fysik, thermodynamics, statistical physics, gravitation, GW approximation, Electron self energy, Green's function, consistency, local-field corrections, vertex function, conserving approximations, variational energies, Mathematical and general theoretical physics, classical mechanics, relativity, quantum mechanics, klassisk mekanik, kvantmekanik, relativitet, statistisk fysik, termodynamik, Fysicumarkivet A:1997:Hindgren
pages
119 pages
publisher
Department of Theoretical Physics, Lund University
defense location
Lecture Hall B, Department of Physics, Lund University, Lund, Sweden
defense date
1997-06-07 10:15
external identifiers
  • Other:ISRN: LUNFD6 / (NTFTF-1034) / 1-33 / (1997)
ISBN
91-628-2555-0
language
English
LU publication?
yes
id
dff2a993-6413-4166-a455-635e82ea9c99 (old id 29390)
date added to LUP
2007-06-13 10:25:47
date last changed
2016-09-19 08:45:07
@misc{dff2a993-6413-4166-a455-635e82ea9c99,
  abstract     = {We study the effects of local vertex corrections to the self energy of the electron gas. We find that a vertex derived from time-dependent density-functional theory can give accurate self energies without including the explicit time dependence of the exchange-correlation potential provided, however, that a proper decay at large momentum transfer (large q) is built into the vertex function. (The local-density approximation for the vertex fails badly.) Total energies are calculated from the Galitskii-Migdal formula and it is shown that a proper large-q behavior, results in a close consistency between the chemical potentials derived from these energies and those obtained directly from the self energy. We show that this internal consistency depends critically on including the same vertex correction in both the self-energy and the screening function. In addition the total energies become almost as accurate as those from elaborate quantum Monte-Carlo (QMC) calculations.<br/><br>
<br/><br>
We also study the accuracy and utility of the functional for the total energy proposed by Luttinger and Ward and a generalization by Almbladh, von Barth, and van Leeuwen. For the electron gas, even the simplest and readily evaluated approximations to these functionals yield total energies of similar quality as those of QMC calculations. The functionals depend on the one-electron Green's function and the screened Coulomb interaction and already rather crude approximations to these quantities produce accurate energies thus demonstrating the insensitivity of the functionals to their arguments.<br/><br>
<br/><br>
Different ways of incorporating vertex corrections beyond the $GW$ level are studied in simple, exactly soluble polaron-like models. We study models of a structureless core electron coupled to valence electrons and a local polaron model by Cini, Hewson and Newns. Our model results indicate that the first vertex correction alone will in general not suffice to improve the spectrum away from the quasi-particle peak. By including a subsequence of Mahan's fractal vertex series, however, we obtain results with correct physical properties which agree better with exact model results.},
  author       = {Hindgren, Mikael},
  isbn         = {91-628-2555-0},
  keyword      = {Matematisk och allmän teoretisk fysik,thermodynamics,statistical physics,gravitation,GW approximation,Electron self energy,Green's function,consistency,local-field corrections,vertex function,conserving approximations,variational energies,Mathematical and general theoretical physics,classical mechanics,relativity,quantum mechanics,klassisk mekanik,kvantmekanik,relativitet,statistisk fysik,termodynamik,Fysicumarkivet A:1997:Hindgren},
  language     = {eng},
  pages        = {119},
  publisher    = {ARRAY(0x8f95a80)},
  title        = {Model Vertices Beyond the GW Approximation},
  year         = {1997},
}