Model Vertices Beyond the GW Approximation
(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 timedependent densityfunctional theory can give accurate self energies without including the explicit time dependence of the exchangecorrelation potential provided, however, that a proper decay at large momentum transfer (large q) is built into the vertex function. (The localdensity approximation for the vertex fails badly.) Total energies are calculated from the GalitskiiMigdal formula and it is shown that a proper largeq 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 timedependent densityfunctional theory can give accurate self energies without including the explicit time dependence of the exchangecorrelation potential provided, however, that a proper decay at large momentum transfer (large q) is built into the vertex function. (The localdensity approximation for the vertex fails badly.) Total energies are calculated from the GalitskiiMigdal formula and it is shown that a proper largeq 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 selfenergy and the screening function. In addition the total energies become almost as accurate as those from elaborate quantum MonteCarlo (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 oneelectron 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 polaronlike 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 quasiparticle 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)
Please use this url to cite or link to this publication:
http://lup.lub.lu.se/record/29390
 author
 Hindgren, Mikael ^{LU}
 opponent

 Prof Rajagopal, A. K., Naval Research Lab., Washington D.C., USA
 organization
 publishing date
 1997
 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, localfield 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
 19970607 10:15
 external identifiers

 other:ISRN: LUNFD6 / (NTFTF1034) / 133 / (1997)
 ISBN
 9162825550
 language
 English
 LU publication?
 yes
 id
 dff2a99364134166a455635e82ea9c99 (old id 29390)
 date added to LUP
 20070613 10:25:47
 date last changed
 20160919 08:45:07
@phdthesis{dff2a99364134166a455635e82ea9c99, abstract = {We study the effects of local vertex corrections to the self energy of the electron gas. We find that a vertex derived from timedependent densityfunctional theory can give accurate self energies without including the explicit time dependence of the exchangecorrelation potential provided, however, that a proper decay at large momentum transfer (large q) is built into the vertex function. (The localdensity approximation for the vertex fails badly.) Total energies are calculated from the GalitskiiMigdal formula and it is shown that a proper largeq 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 selfenergy and the screening function. In addition the total energies become almost as accurate as those from elaborate quantum MonteCarlo (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 oneelectron 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 polaronlike 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 quasiparticle 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 = {9162825550}, keyword = {Matematisk och allmän teoretisk fysik,thermodynamics,statistical physics,gravitation,GW approximation,Electron self energy,Green's function,consistency,localfield 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 = {Department of Theoretical Physics, Lund University}, school = {Lund University}, title = {Model Vertices Beyond the GW Approximation}, year = {1997}, }