Particle-hole self-energy

B The dynamic particle-hole self energy C The zeroth-order degenerate states D First order self energy... 

A Formal definition of the Hilbert space Y B Static particle-particle self energy for electrons C Static particle-hole self energy for electrons... 

The first order of the particle-hole self energy is readily obtained from the expression (68) by replacing the reference states and i ) by their zeroth orders ) and respectively, and by considering the interaction part... 

In a recent publication we have investigated this first order approximation to the particle-hole self energy for the choice y>) = o ) for the reference state tp) and starting from a Hartree-Fock zeroth order [21]. This particular approximation to the particle-hole self energy is referred to as First Order Static Excitation Potential (FOSEP). In terms of the matrix elements of the Hamiltonian the FOSEP approximation of the primary block H reads... 

APPENDIX C STATIC PARTICLE-HOLE SELF ENERGY FOR... 

In this appendix we present the interaction part (at,a, y o, a,<) of the static particle-hole self energy discussed in Sec. VIC. We assume Coulomb interacting electrons with the usual position space representation (106) of the two-body interaction V. The expression for the interaction part of the static self particle-hole self energy can then be readily evaluated, either from the definitions of the extended states (1) or from Eq. (68) ... 

FIGURE 5.5. Virtual excitations contributing to the electron and hole self-energies [2 + )(e) and 2 + >(h), respectively] in the (N + 1)-particle state. 

TABLE 5.4. Different Physical Quantities Contributing to the Formation of the Quasi-Particle Energy-Band Gap in the Alternating trans PA One-Particle Energies e(HF), Electron and Hole Self-Energies, 2(e) and 2(h), Respectively, and Quasi-Particle Energies e(QP)<2 > ... 

Figure 1 Virtual excitations contributing to the electron and hole self-energies particle state...

The structures of Eq. (2.20) would be similar to that of Eq. (2.33) if n°((A)) in Eq. (2.20) is retained. This is approximately Frue in most cases. The major difference would be that would be replaced by in Eqs. (2.33). Since uJpj differs from IaJ ° by the renormalization effects coming from the particle or hole self-energies, an investigation of the selfenergies would yield these effects. Also, it is clear from the structure of Eqs. (2.33) and (2.34) that K(c0) contains the... 

In this section, we describe our model, and give a brief, self-contained account on the equations of the non-equilibrium Green function formalism. This is closely related to the electron and particle-hole propagators, which have been at the heart of Jens electronic structure research [7,8]. For more detailed and more general analysis, see some of the many excellent references [9-15]. We restrict ourselves to the study of stationary transport, and work in energy representation. We assume the existence of a well-defined self-energy. The aim is to solve the Dyson and the Keldysh equations for the electronic Green functions ... 

In the last configuration a particle-hole pair is considered in the system promoting an electron from the valence band (i = h) to a conduction band (i = e). For this reason the method is also called constrained DFT. The excitation energy of the many-electron system is the difference in total energy between two self-consistent calculations with the occupations described above, i.e. ... 

Self-Energy and Spectral Function for a Core Hole. The Quasi-Particle Picture... 

We shall now break down the renormalized self-energy diagram in Fig. 19 c in terms of effective two-body interactions suitable for explicit calculations. In analogy with the Dyson equation in Fig. 19 a, the total three-body, i.e. one-particle-two-hole (phh),... 

In Eq. (5), G is the one-particle Green s function, W is the screened Coulomb interaction and 5 = 0. The real part of the self-energy contains a screened exchange contribution, which requires an explicit calculation of the dielectric matrix of the system, and a Coulomb-hole term which takes into account the actual presence of the quasi-particle (excess electron or hole) in the system and its screening by the surrounding electrons. 

In a recent publication [21], we have shown that already the simplest approximation to the self energy of the extended particle-hole propagator yields a well-behaved, hermitian approximation scheme that removes... 

This equation yields a closed expression for the static self energy. The physical significance is to account for interactions and exchange phenomena between the two test particles (or holes) and the (static) particle density of isolated N-particle system. Also the additional (unphysical) components of the extended states take some effect here as well. The discussion of the static self energy and its physical significance will be the main objective of the rest of this paper. 

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