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Physical review. B, Condensed matter

Van Hove correlation functions for identical fermions: Effects of interactions

Andreas Schinner

Published Feb 1, 1990• 2 citations
Publisher

Abstract

The self part of the dynamic structure factor for three-dimensional jellium is investigated within first-order perturbation theory. It is shown that using a screened Thomas-Fermi potential instead of the pure Coulomb interaction significantly reduces the breakdown range of the model to approximately q\ensuremath{\ll}\ensuremath{\surd}${r}_{s}$ ${k}_{f}$. .AE

DOI
10.1103/physrevb.41.2524

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The self part of the dynamic structure factor for three-dimensional jellium is investigated within first-order perturbation theory. It is shown that using a screened Thomas-Fermi potential instead of the pure Coulomb interaction significantly reduces the breakdown range of the model to approximately q\ensuremath{\ll}\ensuremath{\surd}rs{r}_{s}rs​ kf{k}_{f}kf​. .AE
The density of states (DOS) of the two-dimensional Hubbard model is calculated in second-order perturbation with respect to the on-site Coulomb interaction U . The direct analytic continuation formula is presented to calculate the self-energy on the real-frequency axis. The momentum as well as the energy integral in the self-energy is seriously carried out with use of the Fast-Fourier-Transformation algorithm. Near the half-filling, the imaginary part of the self-energy becomes proportional to the energy in the vicinity of the Fermi level in our weak-coupling calculation. In the interacting case, the van Hove singularity (VHS) in DOS is smeared by the self-energy effect, but there still exists a sharp peak structure due to VHS.
For a quantum system of identical fermions a partition of the density-density correlation function in its ``self'' and ``distinct'' part is presented. These quantities show different properties than their classical counterparts, e.g., they violate the ``detailed balance'' and are not necessarily real. Nevertheless it can be expected that they will provide a good tool for a better description of the self-motion in many-particle systems and are therefore investigated in second-order perturbation theory of the interparticle potential.
In this lecture we present many-body perturbation theory as a method to determine quasiparticle excitations in solids, especially electronic band structures, accurately from first principles.The main ingredient is the electronic self-energy that, in principle, contains all many-body exchange and correlation effects beyond the Hartree potential.As its exact mathematical expression is unknown, approximations must be used in practical calculations.The approximation is obtained using a systematic algebraic approach on the basis of Green function techniques.It constitutes an expansion of the self-energy up to linear order in the screened Coulomb potential, which describes the interaction between the quasiparticles and includes dynamic screening through the creation of exchange-correlation holes around the bare particles.The implementation of the approximation relies on a perturbative treatment starting from density functional theory.Besides a detailed mathematical discussion we focus on the underlying physical concepts and show some illustrative applications.