Anatomy of the Self Energy

Abstract

The general problem of representing the Greens function $G(k,z)$ in terms of self energy, in field theories lacking Wick's theorem, is considered. A simple construction shows that a Dyson like representation with a self energy $\Sigma (k,z)$ is always possible, provided we start with a spectral representation for $G(k,z)$ for finite sized systems and take the thermodynamic limit. The self energy itself can then be iteratively expressed in terms of another higher order self energy, capturing the spirit of Mori's formulation. We further discuss alternative and more general forms of $G(k,z)$ that are possible. In particular, a recent theory by the author of extremely correlated Fermi liquids at density "$n$", for Gutzwiller projected non canonical Fermi operators obtains a new form of the Greens function: $$G(k,z)=\frac{\{1-\frac{n}{2}\}+\Psi (k,z)}{z-{\hat{E}}_k-\Phi (k,z)},$$ with {\em a pair of self energies} $\Phi (z)$ and $\Psi (z)$. Its relationship with the Dyson form is explored. A simple version of the two self energy model was shown recently to successfully fit several data sets of photoemission line shapes in cuprates. We provide details of the unusual spectral line shapes that arise in this model, with the characteristic skewed shape depending upon a single parameter. The EDC and MDC line shapes are shown to be skewed in opposite directions, and provide a testable prediction of the theory.

Published version 27 pages, 11 figures

References in corpus (2)

• Extremely Correlated Fermi Liquids
• Extremely Correlated Fermi Liquid Description of Normal State ARPES in Cuprates

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• Extremely correlated fermi liquid of $t$-$J$ model in two dimensions
• Electronic spectral properties of the two-dimensional infinite-U Hubbard model
• Diagrammatic $\lambda$ series for extremely correlated Fermi liquids
• The splitting of electrons and violation of the Luttinger sum rule
• Method for reconstructing the self-energy from the spectral function
• Dielectric response of electrons with strong local correlations and long-ranged Coulomb interactions