Model Vertices Beyond the GW Approximation
Research output: Thesis › Doctoral Thesis (compilation)
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.
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.
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.
Details
Authors  

Organisations  
Research areas and keywords  Subject classification (UKÄ) – MANDATORY
Keywords

Original language  English 

Qualification  Doctor 
Awarding Institution  
Supervisors/Assistant supervisor 

Award date  1997 Jun 7 
Publisher 

Print ISBNs  9162825550 
Publication status  Published  1997 
Publication category  Research 
Bibliographic note
Defence details
Date: 19970607
Time: 10:15
Place: Lecture Hall B, Department of Physics, Lund University, Lund, Sweden
External reviewer(s)
Name: Rajagopal, A. K.
Title: Prof
Affiliation: Naval Research Lab., Washington D.C., USA
